Abstract
A brief historical background of the development of the absolute stability theory was presented, and some of its methods and approaches, as well as the results obtained using them, were discussed. The kinds of systems under consideration are named, and applications of the methods and results of the absolute stability theory to other scientific and practical fields for solution of the engineering, mechanical, physical, and other problems were presented.
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List of cited literature
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Monographs
Lur’e, A.I., Nekotorye nelineinye zadachi teorii avtomaticheskogo regulirovaniya (Some Nonlinear Problems of the Automatic Control Theory), Moscow: Gostekhizdat, 1951.
Pliss, V.A., Nekotorye problemy teorii ustoichivosti duizheniya v tselom (Some Problems of the Theory of Motion Stability in Large), Leningrad: Leningr. Gos. Univ., 1958.
Letov, A.M., Ustoichivost’ nelineinykh reguliruemykh sistem (Stability of the Nonlinear Controlled Systems), Moscow: Fizmatgiz, 1962.
Aizermanm, M.A. and Gantmakher, F.R., Absolyatnaya ustoichivost’ reguliruemykh sistem (Absolute Stability of the Controlled Systems), Moscow: Akad. Nauk SSSR, 1963.
Pliss, V.A., Nelokal’nye problemy teorii kolebanii (Nonlocal Problems of the Oscillation Theory), Moscow: Nauka, 1964.
La Salle, J.P. and Lefschets, S., Stability by Lyapunov’s Direct Method, New York: Academic, 1961. Translated under the title Issledovanie ustoichivosti pryamym metodom Lyapunova, Moscow: Mir, 1964.
Barbashin, E.A., Vvedenie v teoriyu ustoichivosti (Introduction to the Stability Theory), Moscow: Nauka, 1967.
Lefschetz, S., Stability of Nonlinear Control Systems, New York: Academic, 1965. Translated under the title Ustoichivost’ nelineinykh sistem automaticheskogo upravleniya, Moscow: Mir, 1967.
Barbashin, E.A., Funktsii Lyapunova (Lyapunov Functions), Moscow: Nauka, 1970.
Popov, V.M., Giperustoichivost’ automaticheskikh sistem (Hyperstability of Automatic Systems), Moscow: Nauka, 1970.
Naumov, B.N., Teoriya nelineinykh avtomaticheskikh sistem (Theory of Nonlinear Automatic Systems), Moscow: Nauka, 1972.
Narendra, K.S. and Taylor, J., Frequency Domain Methods for Absolute Stability, New York: Academic, 1973.
Kuntsevich, V.M. and Lychak, M.M., Sintez avtomaticheskogo upravleniya s pomoshch’yu funktsii Lyapunova (Design of Automatic Control by the Lyapunov Functions), Moscow: Nauka, 1977.
Yakubovich, V.A., Leonov, G.A., and Gelig, A.Kh., Ustoichivost’ nelineinykh sistem s needinstvennym sostoyaniem ravnovesiya (Stability of the Nonlinear Systems with Nonunique Equilibrium State), Moscow: Nauka, 1978.
Shil’man, S.V., Metod proizvodyashchikh funktsii v teorii dinamicheskikh sistem (Method of Generating Functions in the Theory of Dynamic Systems), Moscow: Nauka, 1978.
Voronov, A.A., Ustoichivost’, upravlyaemost’, nablyudaemost’ (Stability, Controllability, Observability), Moscow: Nauka, 1979.
Jury, E.I., Innors and Stability of Dynamic Systems, New York: Wiley, 1974. Translated under the title Innory i ustoichivost’ dinamicheskikh sistem, Moscow: Nauka, 1979.
Rouche, N., Habets, P., and Laloy, M., Stability Theory by Liapunov’s Direct Method, New York: Springer-Verlag, 1977. Translated under the title Pryamoi metod Lyapunova v teorii ustoichivosti, Moscow: Mir, 1980.
Aisagaliev, S.A., Analiz i sintez avtonomnykh nelineinykh sistem avtomaticheskogo upravleniya na osnove vtorogo methoda Lyapunova (Analysis and Design of the Automatic Control Systems by the Second Method of Lyapunov), Alma-Ata: Nauka, 1980.
Gelig, A.Kh., Dinamika impul’snykh sistem i neironnykh setei (Dynamics of Pulse Systems and Neural Networks), Leningrad: Leningr. Gos. Univ., 1982.
Rezvan, V., Absolyutnaya ustoichivost’ avtomaticheskikh sistem s zapazdyvaniem (Absolute Stability of the Automatic Delay Systems), Moscow: Nauka, 1983.
Kosyakin, A.A. and Shmarikov, B.M., Kolebaniya v tsifrovykh avtomaticheskikh sistemakh (Oscillations in Automatic Digital Systems), Moscow: Nauka, 1983.
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Metod vektornykh funktsii Lyapunova v teorii ustoichivosti (Method of the Lyapunov Vector Functions in the Stability Theory), Voronov, A.A. and Matrosov, V.M., Eds., Moscow: Nauka, 1987.
Korenevskii, D.G., Ustoichivost’ dinamicheskikh sistem pri sluchainykh vozmushcheniyakh parametrov. Algebraicheskie kriterii (Stability of Dynamic Systems under Random Perturbations of Parameters), Kiev: Naukova Dumka, 1989.
Tsikunov, A.M., Kvadratichnyi kriterii absolyutnoi ustoichivosti v teorii adaptivnykh sistem (Quadratic Absolute Stability Criterion in the Theory of Adaptive Systems), Frunze: Ilim, 1990.
Barkin, A.I., Zelentsovskii, A.L., and Pakshin, P.V., Absolyutnaya ustoichivost’ determinirovannykh i stokhasticheskikh sistem upravleniya (Absolute Stability of the Deterministic and Stochastic Control Systems), Moscow: Mosk. Aviats. Inst., 1992.
Gelig, A.Kh. and Churilov, A.N., Ustoichivost’ i kolebaniya nelineinykh impul’snykh sistem (Stability and Oscillations of the Nonlinear Pulse Systems), St. Petersburg: S.-Peterburg. Gos. Univ., 1993.
Pakshin, P.V., Diskretnye sistemy so sluchainymi parametrami i strukturoi (Discrete Systems with Random Parameters and Structure), Moscow: Nauka, 1994.
Leonov, G.A., Burkin, I.M., and Shepelyavyi, A.I., Frequency Methods in Oscillation Theory, Dordrecht: Kluwer, 1995.
Leonov, G.A., Ponomarenko, D.V., and Smirnova, V.B., Frequency Methods for Nonlinear Analysis. Theory and Applications, Singapore: World Scientific, 1996.
Leonov, G.A. and Smirnova, V.B., Matematicheskie problemy teorii fazovoi sinkhronizatsii (Mathematical Problems of the Phase Synchronization Theory), St. Petersburg: Nauka, 2000.
Pyatnitskii, E.S., Izbrannye trudy. Teoriya upravleniya (Selected Works. Control Theory), Moscow: Fizmatlit, 2004, vol. 1.
Yakubovich, V.A., Leonov, G.A., and Gelig, A.Kh., Stability of Stationary Sets in Control Systems with Discontinuous Nonlinearities, Singapore: World Scientific, 2004.
Ivanov, V.A., Kupreev, S.A., and Liberzon, M.R., Kosmicheskie trosovye sistemy. Nekotorye aspekty prakticheskogo ispol’zovaniya (Space Cable Systems. Some Aspects of Practical Use), Liberzon, M.R., Ed., Moscow: Ross. Inzh. Akad., 2005.
Manulas and Textbooks
Aizerman, M.A., Teoriya avtomaticheskogo regulirovaniya (Theory of Automatic Control), Moscow: Nauka, 1966.
Roitenberg, Ya.N., Avtomaticheskoe upravlenie (Automatic Control), Moscow: Nauka, 1971.
Zubov, V.N., Lektsii po teorii upravleniya (Lectures on the Control Theory), Moscow: Nauka, 1975.
Popov, E.P., Teoriya nelineinykh sistem avtomaticheskogo regulirovaniya i upravleniya (Theory of Nonlinear Systems of Automatic Regulation and Control), Moscow: Nauka, 1979.
Voronov, A.A., Osnovy teorii avtomaticheskogo upravleniya. Osobye lineinye i nelineinye sistemy (Fundamentals of the Automatic Control Theory. Special Linear and Nonlinear Systems), Moscow: Energiya, 1981.
Netushil, A.V., Teoriya avtomaticheskogo upravleniya (Theory of Automatic Control), Moscow: Vysshaya Shkola, 1983.
Pervozvanskii, A.A., Kurs teorii avtomaticheskogo upravleniya (Course of the Automatic Control Theory), Moscow: Nauka, 1986.
Spravochnik po teorii avtomaticheskogo upravleniya (Handbook of the Theory of Automatic Control), Krasovskii, A.A., Ed., Moscow: Nauka, 1987.
Vidyasagar, M., Nonlinear Systems Analysis, Englewood Cliffs: Prentice Hall, 1993.
Leonov, G.A., Mathematical Problems of Control Theory, Singapore: World Scientific, 2001.
Khalil, H., Nonlinear Systems, Upper Saddle River: Prentice Hall, 2003.
Aleksandrov, V.V., Boltyanskii, V.G., Lemak, S.S., et al., Optimal’noe upravlenie dvizheniem (Optimal Control of Motion), Moscow: FIZMATLIT, 2005.
Reviews
Gantmakher, F.R. and Yakubovich, V.A., Absolute Stability of the Nonlinear Controlled Systems, in Tr. II Vses. s”ezda po teoreticheskoi i prikladnoi mekhanike (Proc. II All-Union Conf. Theoret. Applied. Mech.), Moscow: Nauka, 1966, pp. 30–63.
Brockett, R.W., The Status of Stability Theory for Deterministic Systems, IEEE Trans. Automat. Control, 1966, vol. AC-11, no. 3, pp. 696–706.
Pyatnitskii, E.S., New Studies on Absolute Stability of Automatic Control Systems, Autom. Telemekh., 1968, no. 6, pp. 5–36.
Levin, A.Yu., Nonoscillation of the Solutions of the Equation x (n) + σ1(t) x (n−1) + ... + σn(t)x + 0, Usp. Mat. Nauk, 1969, vol. 24, no. 2 (146), pp. 43–96.
Matrosov, V.M., Method of the Lyapunov Vector Functions in Feedback Systems, Avtom. Telemekh., 1972, no. 9, pp. 63–75.
Matrosov, V.M., Method of the Lyapunov Vector Functions in Analysis of Complex Distributed-parameter Systems, Avtom. Telemekh., 1973, no. 1, pp. 5–22.
Yakubovich, V.A., Methods of the Theory of Absolute Stability, in Metody issledovaniya nelineinykh sistem avtomaticheskogo upravleniya (Methods of Studying the Nonlinear Automatic Control Systems), Nelepin, R.A., Ed., Moscow: Nauka, 1975, pp. 74–174.
Yakubovich, V.A., Frequency Methods of Qualitative Study of the Nonlinear Controllable Systems, in VII Int. Konf. über nichtlineare Schwingungen, Berlin: Akademie, 1977, vol. 1, pp. 365–387.
Venkatesh, Y.V., A Survey of some Recent Results in the Stability and Instability Analyses of Time-varying Systems, Int. J. Non-linear Mech., 1977, vol. 12, no. 4, pp. 251–268.
Alekseevskaya, N.L. and Gromova, P.S., The Second Lyapunov Method for the Differential Equations with Divergent Argument, in Differents, uravneniya s otklonyayushchimsya argumentom (Differential Equations with Divergent Argument), Kiev: Akad. Nauk USSR, 1977, pp. 19–34.
Zharkov, A.V. and Yakubovich, V.A., Quadratic Criterion for Conditional Absolute Stability and its Use, Dinamika Sistem, 1977, vol. 12, pp. 54–67.
Liberzon, M.R., New Results on Absolute Stability of the Nonstationary Controlled Systems (Review), Avtom. Telemekh., 1979, no. 8, pp. 29–48.
Ferrante, L. and Marchetti, F., Some Results on Total Stability, Boll. Unione Mat. Ital., 1981, vol. A18, no. 3, pp. 111–122.
Parks, P.S., Stability of Systems—A Survey, Proc. Int. Conf. Contr. Appl., Warwick, 1981, pp. 266–277.
Voronov, A.A., State-of-the-art and Problems of the Stability Theory, Avtom. Telemekh., 1982, no. 5, pp. 5–28.
Likhtarnikov, A.L. and Yakubovich, V.A., Absolute Stability of the Automatic Delay Systems. Supplement to the book of Rezvan Absolyutnaya ustoichivost’ nelineinykh sistem s zapazdyvaniem (Absolute Stability of the Nonlinear Delay Systems), Moscow: Nauka, 1983, pp. 287–355.
Barabanov, N.E., Gelig, A.Kh., Leonov, G.A., et al., The Frequency Theory (Yakubovich-Kalman Lemma) in the Control Theory, Avtom. Telemekh., 1996, no. 10, pp. 3–40.
Liberzon, M.R., Lur’e Problem of Absolute Stability—A historical Essay, Proc IFAC Symposium Nonlinear Control Systems NOLCOS’01, St. Petersburg, 2001, vol. 1, pp. 22–25.
Liberzon, M.R., Absolute Stability of Dynamical Systems (Survey), Proc. IFAC World Congr., Barcelona, 2002, vol. 1, pp. 265–268.
Publications of the Results 1942
Bulgakov, B.V., Self-Oscillations of the Controlled Systems, Dokl. Akad. Nauk SSSR, 1942, vol. 37, no. 9, pp. 283–287.
1946
Bulgakov, B.V., Some Problems of the Theory of Control with Nonlinear Characteristics, Prikl. Mat. Mekh., 1946, vol. 10, no. 3, pp. 313–332.
Bulgakov, B.V., On Accumulation of Perturbations in the Linear Oscillatory Systems with Constant Parameters, Dokl. Akad. Nauk SSSR, 1946, vol. 51, no. 5, pp. 339–342.
1949
Aizerman, M.A., On a Problem Concerning Stability “in Large” of the Dynamic Systems, Usp. Mat. Nauk, 1949, vol. 4, no. 4, pp. 186–188.
1950
Bulgakov, B.V. and Kuzovkov, N.T., On Accumulation of Perturbations in the Linear Systems with Variable Parameters, Prikl. Mat. Mekh., 1950, vol. 14, pp. 7–12.
Erugin, N.P., Some Issues of Motion Stability and Qualitative Theory of Differential Equations in Large, Prikl. Mat. Mekh., 1950, vol. 14, pp. 459–512.
1951
Malkin, I.G., On the Stability Theory of the Controlled Systems, Prikl. Mat. Mekh., 1951, vol. 15, pp. 59–66.
1952
Krasovskii, N.N., Theorems of Stability of Motions Obeying a System of Differential Equations, Prikl. Mat. Mekh., 1952, vol. 16, pp. 547–554.
1953
Krasovskii, N.N., On Stability of Solutions of the System of Two Differential Equations, Prikl. Mat. Mekh., 1953, vol. 17, pp. 651–672.
1957
Kalman, R.E., Physical and Mathematical Mechanisms of Instability in Nonlinear Automatic Control Systems, Trans. ASME, 1957, no. 79, pp. 553–566.
1961
Popov, V.M., On Absolute Stability of Nonlinear Automatic Control Systems, Avtom. Telemekh., 1961, no. 8, pp. 961–979.
1962
Tsypkin, Ya.Z., On Stability in Large of the Nonlinear and Pulse Automatic Systems, Dokl. Akad. Nauk SSSR, 1962, vol. 145, no. 10, pp. 52–55.
Yakubovich, V.A., Solution of some Matrix Inequalities Encountered in the Automatic Control Theory, Dokl. Akad. Nauk SSSR, 1962, vol. 143, no. 6, pp. 1304–1307.
1963
Yakubovich, V.A., Frequency Conditions for Absolute Stability of the Controlled Systems with Hysteresis Nonlinearities, Dokl. Akad. Nauk SSSR, 1963, vol. 149, no. 2, pp. 288–291.
Yakubovich, V.A., Absolute Stability of the Nonlinear Systems of Automatic Control in the Critical Cases. I, II, Avtom. Telemekh., 1963, vol. 24, no. 3, pp. 293–302; no. 6, pp. 717–731.
Kalman, R.E., Lyapunov Functions for the Problem of Lur’e in Automatic Control, Proc. USA National Acad. Sci., 1963, vol. 49, no. 1, pp. 201–205.
1964
Yakubovich, V.A., Solution of some Matrix Inequalities Encountered in the Nonlinear Control Theory, Dokl. Akad. Nauk SSSR, 1964, vol. 156, no. 2, pp. 278–281.
Yakubovich, V.A., Absolute Stability of the Nonlinear Systems of Automatic Control in the Critical Cases. III, Avtom. Telemekh., 1964, vol. 25, no. 5, pp. 601–612.
Yakubovich, V.A., Method of Matrix Inequalities in the Theory of Stability of the Nonlinear Controllable Systems. I. Absolute Stability of Forced Oscillations, Avtom. Telemekh., 1964, vol. 25, no. 7, pp. 1017–1029.
Brockett, R.W. and Forys, L.J., On the Stability of Systems Containing a Time-varying Gain, Proc. II Ann. Allerton Conf. Circuit Syst. Theory, Urbana, 1964, vol. 3, pp. 413–430.
1965
Yakubovich, V.A., Frequency Conditions for Absolute Stability and Dissipativeness of the Controllable Systems with One Differentiable Nonlinearity, Dokl. Akad. Nauk SSSR, 1965, vol. 160, no. 2, pp. 298–301.
Yakubovich, V.A., Method of Matrix Inequalities in the Theory of Stability of the Nonlinear Controllable Systems. II, III, Avtom. Telemekh., 1965, vol. 26, no. 4, pp. 577–599; no. 5, pp. 763–768.
1966
Fitts, R.E., Two Counterexamples to Aizerman’s Conjecture, IEEE Trans. Automat. Control, 1966, vol. AC-11, pp. 553–556.
1967
Yakubovich, V.A., Frequency Conditions for Absolute Stability of the Control Systems with Multiple Nonlinear or Linear Nonstationary Units, Avtom. Telemekh., 1967, vol. 23, no. 6, pp. 5–30.
Yakubovich, V.A., Absolute Stability of the Pulse Systems with Multiple Nonlinear or Linear Nonstationary Units. I, Avtom. Telemekh., 1967, no. 9, pp. 59–72.
Yakubovich, V.A., Frequency Conditions for Stability of Nonlinear Integral Equations of Automatic Control, Vestn. Leningr. Gos. Univ., 1967, vol. 7, no. 2, pp. 103–125.
Brockett, R.W. and Lee, H.B., Frequency-domain Instability Criteria for Time-varying and Nonlinear Systems, Proc. IEEE, 1967, vol. 55, no. 5, pp. 604–619.
1968
Yakubovich, V.A., Absolute Stability of the Pulse Systems with Multiple Nonlinear or Linear Nonstationary Units. II, Avtom. Telemekh., 1968, no. 2, pp. 81–101.
Yakubovich, V.A., On the Pulse Control Systems with Width Modulation, Dokl. Akad. Nauk SSSR, 1968, vol. 180, no. 2, pp. 283–294.
Willems, J.L. and Willems, J.C., Stability Analysis of Nonlinear Control Systems in the Frequency Domain, Messen Steuern Regeln, 1968, vol. 11, no. 3, pp. 114–116.
1969
Yakubovich, V.A., On a Class of Nonlinear Differential Equations for which the Questions of Stability in Large and Instability Can be Solved Effectively, Dokl. Akad. Nauk SSSR, 1969, vol. 186, no. 5, pp. 1027–1030.
1970
Leonov, G.A., On Necessity of the Frequency Condition for Absolute Stability of the Stationary Systems in the Critical Case of a Pair of Purely Imaginary Roots, Dokl. Akad. Nauk SSSR, 1970, vol. 193, no. 4, pp. 756–759.
Pyatnitskii, E.S., Absolute Stability of the Nonstationary Nonlinear Systems, Avtom. Telemekh., 1970, no. 1, pp. 5–15.
Pyatnitskii, E.S., Absolute Stability of the Nonstationary Nonlinear Systems. Free and Forced Motions, Avtom. Telemekh., 1970, no. 3, pp. 5–15.
Pyatnitskii, E.S., Absolute Stability of the Nonlinear Pulse Systems with Nonstationary Nonlinearity, Avtom. Telemekh., 1970, no. 8, pp. 50–58.
Yakubovich, V.A., Solution of one Algebraic Problem Encountered in the Control Theory, Dokl. Akad. Nauk SSSR, 1970, vol. 193, no. 1, pp. 57–60.
Yakubovich, V.A., Absolute Instability of Nonlinear Control Systems. I, Avtom. Telemekh., 1970, no. 12, pp. 5–14.
Willems, J.L. and Willems, J.C., The Application of Lyapunov Methods to the Computation of Transient Stability Regions for Multimachine Power Systems, IEEE Trans. Power Apparatus Syst., 1970, vol. PAS-89, no. 5–6, pp. 795–801.
1971
Yakubovich, V.A., S-procedure in the Nonlinear Control Theory, Vestn. Leningr. Gos. Univ., ser. 1, 1971, no. 1, pp. 62–77.
Yakubovich, V.A., Absolute Instability of the Nonlinear Control Systems. II. Systems with Nonstationary Nonlinearities. Circular criterion, Avtom. Telemekh., 1971, no. 6, pp. 25–33.
Willems, J.C. and Blankenship, G.L., Frequency Domain Stability Criteria for Stochastic Systems, IEEE Trans. Automat. Control, 1971, vol. AC-16, no. 4, pp. 292–299.
1973
Zhermolenko, V.N., Absolute Stability of One Class of Third-order Systems, in Nauchn. tr. aspir. mekhmata Mosk Gos. Univ. (Collected Papers of the Postgraduates of the Department of Mathematics and Mechanics of the Moscow State Univ.), Moscow: Mosk. Gos. Univ., 1973, pp. 160–167.
Pyatnitskii, E.S., On Uniform Stability under Parametric Perturbations, Diff. Uravn., 1973, vol. 9, no. 7, pp. 1262–1273.
Yakubovich, V.A., Frequency Theorem in the Control Theory, Sib. Mat. Zh., 1973, vol. 14, no. 2, pp. 384–420.
Yakubovich, V.A. and Fradkov, A.L., Necessary and Sufficient Conditions for Absolute Stability in the Classes of Systems with Two Integral Quadratic Constraints, Dokl. Akad. Nauk SSSR, 1973, vol. 213, no. 4, pp. 798–901.
1974
Willems, J.C. and Brockett, R.W., Average Value Symmetry Criteria for Symmetric Systems, Ricerche Automatica, 1974, vol. 4, no. 2–3, pp. 87–108.
1975
Aleksandrov, V.V. and Zhermolenko, V.N., A Criterion for Absolute Stability of the Third-order Systems, Dokl. Akad. Nauk SSSR, 1975, vol. 222, no. 2, pp. 309–311.
Aleksandrov, V.V. and Zhermolenko, V.N., Absolute Stability of the Third-order Systems with a Nonlinear Nonstationary Element, in Nauchn. tr. NII MEKH MGU (Proc. NII MEKH MGU), 1975, no. 40, pp. 48–64.
Leonov, G.A., Stability and Oscillations in the Phase Systems, Sib. Mat. Zh., 1975, vol. 16, no. 5, pp. 1031–1052.
1976
Bendrikov, G.A. and Sidorova, G.A., Using the Method of Root Trajectories to Study the Nonlinear Systems for Absolute Stability by the V.M. Popov Criterion, Vestn. Mosk. Gos. Univ., 1976, no. 2, pp. 177–186.
Leonov, G.A., On a Class of Dynamic Systems with Cylindrical Phase Space, Sib. Mat. Zh., 1976, vol. 17, no. 1, pp. 91–112.
Skachkov, B.N., Development of the Lyapunov Function for the Self-control Systems, Diff. Uravn., 1976, vol. 12, no. 8, pp. 1452–1461.
Cartianu, Gh. and Pilat, F.L., Extension of Applicability of Popov’s Steady-state Absolute-stability Frequency Criterion of Nonlinear Systems, Probl. Automatizare, 1976, vol. 9, pp. 97–105.
Datta, K.B., On the Stability of Discrete Multivariable Lur’e Problem, J. Inst. Electronics & Telecommun. Eng., 1976, vol. 22, no. 1, pp. 15–17.
Datta, K.B., Absolute Stability of Pulse-width Modulated Feedback Systems Containing an Integrator, J. Inst. of Electronics & Telecommun. Eng., 1976, vol. 22, no. 9, pp. 591–594.
1977
Voronov, A.A., Systems with Differentiable Nondecreasing Nonlinearity that are Absolutely Stable in the Hurwitzian Angle, Dokl. Akad. Nauk SSSR, 1977, vol. 234, no. 1, pp. 38–41.
Gromova, P.S. and Pelevina, A.F., Absolute Stability of the Automatic Control Delay Systems, Diff. Uravn., 1977, vol. 13, no. 8, pp. 1375–1383.
Zhermolenko, V.N. and Lokshin, B.Ya., On Stability of Nonstationary Motion of the Axially Symmetric Flight Vehicle, Mekh. Tverd. Tela, 1977, no. 5, pp. 32–39.
Koryakin, Yu.A. and Leonov, G.A., Frequency Conditions for Stability in Large of the Multivariable Phase Systems, in Problemy teorii periodicheskikh dvizhenii (Problems of the Theory of Periodic Motions), Izhevsk, 1977, pp. 61–64.
Krasnosel’skii, M.A. and Pokrovskii, A.V., Principle of no Bounded Solutions in the Problem of Absolute Stability, Dokl. Akad. Nauk SSSR, 1977, vol. 233, no. 3, pp. 293–296.
Leonov, G.A., Reduction Theorem for the Nonstationary Nonlinearities, Vestn. Leningr. Gos. Univ., 1977, no. 7, pp. 38–42.
Leonov, G.A. and Churilov, A.N., On Stability in Large of the Phase Delay Systems, in Problemy teorii periodicheskikh dvizhenii (Problems of the Theory of Periodic Motions), Izhevsk, 1977, pp. 65–66.
Leonov, G.A. and Chshieva, T.L., On Stability of a Class of Phase Systems with Two Nonlinearities, Izv. Akad. Nauk Kaz. SSR, Fiz. Mat., 1977, no. 3, pp. 76–78.
Shil’man, S.V., Algebraic Criterion for Absolute Stability of the Nonlinear Discrete Systems, Avtom. Telemekh., 1977, vol. 38, no. 12, pp. 48–55.
Alexandrov, V.V., Carton, R.H., and Betancourt, M.M., Estabilidad absoluta de los sistemas lineales de secondo orden con coeficientes variables, Investic Oper., 1977, no. 20, pp. 21–37.
Bickart, T.A. and Jury, E.I., Regions of Polynomial Root Clustering, J. Franklin Inst., 1977, vol. 304, no. 4/5, pp. 149–160.
Jumarie, G., Stochastic Hyperstability for a Broad Class of Distributed Systems with Space Dependent Coefficients, Ricerche Automatica, 1988, vol. 8, no. 2–3, pp. 163–92.
1978
Alekseev, A.S. and Chubarov, M.A., On Numerical-and-Analytical Construction of the Absolute Stability Domains, Diff. Integr. Uravn., 1978, no. 2, pp. 101–108.
Akhmerov, R.R., Kazakova, N.G., and Pokrovskii, A.V., Principle of no Constrained Solutions and Absolute Stability of the Neutral-type Equations, Serdika B”m. Mat. Spis., 1978, vol. 4, no. 1, pp. 61–69.
Blyagoz, Z.U. and Leonov, G.A., Frequency Criterion for Stability in Large of the Nonlinear Systems, Vestn. Leningr. Gos. Univ., 1978, no. 13, pp. 18–23.
Brusin, V.A., Design of a Searchless Self-adjusting System by the Method of the Absolute Stability Theory, Avtom. Telemekh., 1978, no. 39, pp. 61–67.
Voronov, A.A., Absolutely Stable Systems with Differentiable Nondecreasing Nonlinearity, Avtom. Telemekh., 1978, no. 7, pp. 12–18.
Kalitin, B.S. and Cherchun, M.Ya., On the Aizerman Problem for the Second-order Systems, Vestn. Byelorus. Univ., 1978, p. 17.
Krasnosel’skii, M.A. and Pokrovskii, A.V., On Absolute Stability of the Discrete-time Systems, Avtom. Telemekh., 1978, no. 2, pp. 42–45.
Lipatov, A.V., Extension of the Circular Criterion for Absolute Stability for a Class of Linear Continuous Nonstationary Systems, Moscow: Mosk. Aviats. Inst., 1978, no. 434, pp. 65–69.
Maigarin, B.Zh. and Kasimov, E.K., Absolute Instability of the Nonlinear Control Systems, Izv. Akad. Nauk Kaz. SSR, Fiz. Mat., 1978, no. 3, pp. 42–48.
Meilakhs, A.M., On Design of Stable Automatic Control Systems under Parametric Perturbations, Avtom. Telemekh., 1978, no. 10, pp. 5–16.
Borne, P. and Gentina, J.C., Absolute Stability for Nonlinear, Nonstationary Large Scale Systems, Proc. 1978 Joint Automatic Control Conf. ISA, 1978, part III, vol. 3–4, pp. 3/317–3/326.
Grujic, L.T., Solutions for the Lurie-Postnikov and Aizerman Problems, Int. J. Syst. Sci., 1978, vol. 9, no. 12, pp. 1359–1372.
Mitra, D., The Absolute Stability of High-order Discrete-time Systems Utilizing the Saturation Nonlinearity, IEEE Trans. Circuits & Syst., 1978, vol. CAS-25, no. 6, pp. 365–371.
Singh, V. and Kumar, A., Verification of Aizerman’s Conjecture for a Class of Non-linear Systems, J. Inst. of Eng. (India) Electronics & Telecommun. Eng. Division, 1976, vol. 59, no. ET-1, pp. 23, 24.
Vidyasagar, M., Some General Necessary and Sufficient Conditions for the Absolute Stability of Nonlinear Feedback Systems, Proc. 1978 IEEE Int. Symp. Circuits Syst., 1978, pp. 620–625.
1979
Abdullaev, A.A. and Dzhafarov, E.M., Frequency Criterion for Stability of Delay SPS, Avtom. Telemekh., 1979, no. 6, pp. 198–205.
Barabanov, N.E., Stability and Instability of the Stationary Sets of Nonlinear Control Systems with Constrained Derivative, Vestn. Leningr. Gos. Univ., 1979, no. 13, pp. 115, 116.
Barabanov, N.E., Absolute Stability of the Control Systems with Monotonic Nonlinearities, Vestn. Leningr. Gos. Univ., Mat. Mekh. Astron., 1979, no. 11.
Barabanov, N.E. and Yakubovich, V.A., Absolute Stability of the Control Systems with One Hysteresis Nonlinearity, Avtom. Telemekh., 1979, no. 12, pp. 5–11.
Gromova, P.S. and Lisana, P.M., Method of the Lyapunov Vector Functions for the Delay Systems, Differents. Uravneniya s Otklonyayushchimsya Argumentom, 1979, no. 11, pp. 14–22.
Leonov, G.A., Abramovich, S.M., Burkina, L.I., et al., Reduction Method in the Theory of Dynamic Systems with Cylindrical Phase Space and its Application to the Studies of Stability of the Electric Power System, in Teoriya ustoichivosti i ee prilozheniya (Stability Theory and its Applications), Novosibirsk: Nauka, 1979, pp. 55–60.
Liberzon, M.R., Absolute Stability of a Class of Control led Systems, Vestn. Mosk. Gos. Univ., Mat. Mech., 1979, no. 3, pp. 74–80.
Liberzon, M.R., Absolute Stability of a Class of Tracking Systems, Avtom. Telemekh., 1979, no. 12, pp. 25–29.
Molchanov, A.P., Absolute Stability of the Pulse Systems with Several Nonstationary Nonlinear Elements, Avtom. Telemekh., 1979, no. 3, pp. 43–51.
Osipov, L.A., Kochetov, S.A., and Konovalov, A.S., Automatic Determination of the Domain of Absolute Stability of the Control Systems with Two Nonlinear Elements, Izv. Vuzov, Prib., 1979, vol. 22, no. 11, pp. 23–28.
Rimskii, G.V., Root Method of Constructing the Domains of Absolute Stability of the Nonlinear Systems, Izv. Vuzov, Elektromekh., 1979, no. 6, pp. 499–503.
Chubarov, M.A., On Criteria of Polynomial Nonnegativeness and Determination of the Absolute Stability Domains, Diff. Integr. Uravn., 1979, pp. 149–157.
Grujic, L.T., Borne, P., and Gentina, J.C., Matrix Approaches to the Absolute Stability of Time-varying Lurie-Postnikov Systems, Int. J. Control, 1979, vol. 30, no. 6, pp. 967–980.
Kaszkurewicz, E. and Hsu, L., Stability of Nonlinear Systems: A Structural Approach, Automatica, 1979, vol. 15, no. 5, pp. 609–614.
Rasvan, V., Absolute Stability of Nonlinear Difference Systems, Revue Romaine des Sciences Techniques, 1979, vol. 24, no. 3, pp. 495–500.
Zhermolenko, V.N. and Hing Corton, R., Etabilidad absoluta de los sistemas de control automatico de seguno orden con coeficientes variables, Investigation Oper., 1979, no. 28, pp. 39–54.
1980
Grujic, L.T., Necessary and Sufficient Lyapunov Conditions for Absolute Stability and the Aizerman Hypothesis, Mat. Fiz., 1980, no. 28, pp. 7–19.
Kiguradze, I.T. and Rozov, N.Kh., On Absolute Stability of Nonlinear Nonstationary Automatic Control Systems, Diff. Uravn., 1980, vol. 16, no. 4, pp. 755–756.
Leonov, G.A., On an Extension of the V.M. Popov Frequency Criterion for Nonstationary Nonlinearities, Avtom. Telemekh., 1980, no. 11, pp. 21–26.
Leonov, G.A. and Smirnova, V.B., Reduction Method for Integro-differential Equations, Sib. Mat. Zh., 1980, no. 4, pp. 112–124.
Liberzon, M.R., On Absolute Stability of Third-order Systems with Two Nonlinear Elements, Vestn. Mosk. Gos. Univ., Mat. Mekh., 1980, no. 3, pp. 88–92.
Lychak, M.M., A New Approach to Studying Stability of the Nonlinear Dynamic Systems, Avtomatika, 1980, vol. 13, no. 1, pp. 38–45.
Meilakhs, A.M., On Stabilization of the Linear Controllable Systems under Constant Acting Perturbations, Avtom. Telemekh., 1980, no. 11, pp. 27–32.
Meilakhs, A.M., On Existence of the Lyapunov Functions for the Parametrically Perturbed Linear Systems, in Slozhnye sistemy upravleniya (Complex Control Systems), Kiev: Inst. Cybern., 1980, pp. 11–15.
Onaibaev, K., Relation between Two Aizerman Problems, in Matem. modelir. i optim. upravl. (Mathematical Modeling and Optimal Control), Alma-Ata: Kazan. Gos. Univ., 1980, pp. 152–155.
Grujic, L.T. and Porter, B., Discrete-time Tracking Systems Incorporating Lur’e Plants with Multiple Nonlinearities, Int. J. Syst. Sci., 1980, vol. 11, no. 12, pp. 1505–1520.
1981
Aizikovich, A.A., Nonoscillation Criteria for the Solutions of the Difference Equation, Diff. Uravn., 1981, vol. 17, no. 12, pp. 2201–2211.
Gil’, M.I., On Stability of the Nonstationary Systems with Distributed Parameters, Avtom. Telemekh., 1981, no. 1, pp. 5–8.
Krasnosel’skii, M.A. and Pokrovskii, A.V., Principle of Lack of Bounded Solutions in the Problem of Absolute Stability, in Ustoichivost’ dvizheniya. Analit. mekh. Upravlenie dvizheniem (Motion Stability, Analytical Mechanics, Control of Motion), Moscow, 1981, pp. 156–169.
Leonov, G.A., The Necessary Frequency Conditions for Absolute Stability of the Nonstationary Systems, Avtom. Telemekh., 1981, no. 1, pp. 15–19.
Leonov, G.A., On Stability in Large of the Nonlinear Systems in the Critical Case of Two Zero Roots, Prikl. Mat. Mekh., 1981, vol. 45, no. 4, pp. 752–755.
Likhtarnikov, A.L., Necessary and Sufficient Conditions for Absolute Stability of the Nonlinear Distributed Systems in Linear Output, in Chislennye metody v gidromekhanike (Numerical Methods in Fluid Mechanics), Leningrad: LISI, 1981, pp. 71–76.
Molchanov, A.P. and Pyatnitskii, E.S., Absolute Instability of the Nonlinear Nonstationary Systems. I, Avtom. Telemekh., 1981, no. 1, pp. 19–27.
Opoitsev, V.I., Unbounded Domains of Asymptotic Stability, Avtom. Telemekh., 1981, no. 3, pp. 5–13.
Skorodinskii, V.I., Absolute Stability and Absolute Instability of the Control Systems with Two Nonlinear Nonstationary Elements. I, Avtom. Telemekh., 1981, no. 9, pp. 21–29.
Datta, K.B. and Chaki, S.R., Absolute Stability of Thyristor Controlled Constant Field Separately Excited DC Motor under Mark-space Control, J. Technology, 1981, vol. 26, no. 1, pp. 41–53.
Grujic, L.T., On Absolute Stability and the Aizerman Conjecture, Automatica, 1981, vol. 17, no. 2, pp. 335–349.
1982
Barabanov, N.E., Existence of Periodic Solutions of the Nonlinear Controlled Systems and Kalman’s Hypothesis, Usp. Mat. Nauk, 1982, vol. 37, no. 1.
Barabanov, N.E., Stability, Instability and Dichotomy of the Control Systems with Gradient Nonlinearities, Avtom. Telemekh., 1982, no. 4, pp. 5–8.
Barkin, A.I. and Zelentsovskii, A.L., Method of Nonlinear Transformation of Coordinates for Studying Absolute Stability of the Control Systems, in Dinamika neodnorodnykh sistem, materialy seminara (Dynamics of Nonuniform Systems. Materials of Seminar), Moscow: VNIISI, 1982, pp. 41–50.
Maigarin, B.Zh., Study of Nonlinear Automatic Systems for Control of Course of Ships and Aircraft, Izv. Akad. Nauk Kaz. SSR, Fiz. Mat., 1982, no. 3, pp. 25–30.
Molchanov, A.P. and Pyatnitskii, E.S., Absolute Instability of the Nonlinear Nonstationary Control Systems. I, II, III, Avtom. Telemekh., 1982, no. 1, pp. 19–27; no. 2, pp. 17–28; no. 3, pp. 29–41.
Rozov, N.Kh., Study of Absolute Stability of the Automatic Control Systems, in: Differents, uravneniya i prilozheniya. Tr. 2-i konf. (Differential Equations and Applications. Proc. 2nd Conf.), Russe, 1982, part 2, pp. 622–627.
Skorodinskii, V.I., Absolute Stability and Absolute Instability of the Control Systems with Two Nonlinear Nonstationary Elements, Avtom. Telemekh., 1982, no. 6, pp. 87–94.
Molchanov, A.P. and Pyatnitsky, E.S., A Variational Method for Investigating Absolute Stability and Absolute Instability of Nonlinear Control Systems, Proc. 8th Triennial World IFAC Congress, Kyoto, 1982, vol. 1, pp. 129–136.
Pyatnitsky, E.S. and Skorodinsky, V.I., Numerical Methods of Lyapunov Function Construction and Their Application to the Absolute Stability Problem, Syst. Control Lett., 1982, vol. 2, no. 2, pp. 130–135.
1983
Gil’, M.I., On a Class of Absolute Stable Systems, Avtom. Telemekh., 1983, no. 10, pp. 70–76.
Gil’, M.I., On a Class of Systems that are Absolutely Stable in the Hurwitzian Angle, Dokl. Akad. Nauk SSSR, 1983, vol. 269, no. 6, pp. 1324–1327.
Zarubin, A.G., Krasnosel’skii, M.A., and Pokrovskii, A.V., On the Principle of Absence of Bounded Modes in the Problem of Absolute Stability of Distributed-parameter Systems, Avtom. Telemekh., 1983, no. 3, pp. 13–19.
Kamenetskii, V.A., Absolute Stability and Absolute Instability of the Control Systems with Several Nonlinear Nonstationary Elements, Avtom. Telemekh., 1983, no. 12, pp. 20–30.
Kamenetskii, V.A. and Pyatnitskii, E.S., Iterative Method of Construction of the Lyapunov Functions and its Numerical Computer-aided Realization, in EVM v problemakh upravleniya. Sb. tr. (Computers in Control Problems, Collected Papers), Moscow: Inst. Probl. Upravlen., 1983, pp. 61–74.
Leonov, G.A., On Boundedness of the Solutions of Nonautonomous Differential Equations, Vestn. Leningr. Gos. Univ., 1983, no. 7, pp. 21–26.
Likhtarnikov, A.L., Dichotomy and Absolute Instability in the Nonlinear Distributed-parameter Systems, in Chislennye metody v zadachakh matem. fiziki (Numerical Methods in the Problems of Mathematical Physics), Leningrad: LISI, 1983, pp. 22–29.
Likhtarnikov, A.L. and Yakubovich, V.A., Abstract Criteria for Absolute Stability of the Nonlinear Systems in Linear Output and Their Use, Sib. Mat. Zh., 1983, vol. 24, no. 5, pp. 129–148.
Meilakhs, A.M., On Control of Rotational Motion of Solid Body, Diff. Uravn., 1983, vol. 19, no. 11, pp. 1860–1866.
Molchanov, A.P., Criterion for Absolute Stability of the Pulse Systems with Nonstationary Nonlinearity, Avtom. Telemekh., 1983, no. 6, pp. 42–45.
Pyatnitskii, E.S. and Skorodinskii, V.I., Numerical Methods of Constructing the Lyapunov Functions and a Criterion for Absolute Stability in the Form of Numerical Procedure, Autom. Telemekh., 1983, no. 11, pp. 52–63.
Yakubovich, V.A., Graphic Criteria for Absolute Stability and Instability of the Nonlinear Control Systems, Dokl. Akad. Nauk SSSR, 1983, vol. 271, no. 2, pp. 307–310.
Yakubovich, V.A., Absolute Stability of the Nonlinear Distributed-parameter Systems, Avtom. Telemekh., 1983, no. 6, pp. 53–61.
Yakubovich, V.A., Abstract Theory of Absolute Stability and its Application, Kibern. Vychisl. Tekh., 1983, pp. 3–8.
Barkin, A.I. and Zelentsovsky, A.L., A New Criterion for Absolute Stability: Nonlinear Transformation Technique, Int. J. Syst. Sci., 1983, vol. 14, no. 10, pp. 1217–1228.
1984
Barkin, A.I., On Relation between Two Criteria for Absolute Stability, Avtom. Telemekh., 1984, no. 1, pp. 36–41.
Barkin, A.I. and Zelentsovskii, A.L., Absolute Stability of the Automatic Control Systems with Single Nonlinearity, Dokl. Akad. Nauk SSSR, 1984, vol. 276, no. 4–6, pp. 809–812.
Leonov, G.A., Method of Nonlocal Reduction in the Theory of Absolute Stability of Nonlinear Systems, Avtom. Telemekh., 1984, no. 3, pp. 48–56.
Leonov, G.A., On One Hypothesis of A.A. Voronov, Avtom. Telemekh., 1984, no. 5, pp. 17–20.
Lipatov, A.V., Stability of the Discrete Stationary System with One Nonlinear Unit, Avtom. Telemekh., 1984, no. 9, pp. 74–83.
Rozov, N.Kh., Three Problems in the Ordinary Differential Equations, Usp. Mat. Nauk, 1984, vol. 39, no. 4, pp. 145, 146.
Skorodinskii, V.I., Absolute Stability of Nonstationary Motion of the Axially Symmetric Rotating Flight Vehicle, Mekh. Tverd. Tela, 1984, no. 3, pp. 17–21.
Speranskaya, L.S., Necessary Frequency Conditions for Absolute Stability of Systems in the Critical Case of a Pair of Purely Imaginary and One Zero Root, in Matematicheskaya fizika (Mathematical Physics), Leningrad: Leningr. Gos. Pedag. Univ., 1984, pp. 46–55.
Kaszkurewicz, E. and Hsu, L., A Note on the Absolute Stability of Non-linear Discrete-time Systems, Int. J. Control, 1984, vol. 40, no. 4, pp. 867–869.
Resende, P. and Kaszkurewicz, E., A New State-space Block-tridiagonal Realization Algorithm for Matrix Transfer Functions and its Use in Absolute Stability Problems, in Proc. 23rd IEEE Conf. Decision Control, 1984, vol. 1, pp. 106–110.
1985
Aleksandrov, V.V. and Morozova, O.I., On the Necessary and Sufficient Conditions for Absolute Stability of the Second-order Systems, Avtom. Telemeekh., 1985, no. 8, pp. 161–164.
Andrusevich, V.V., On a Class of Absolutely Stable Nonlinear Nonstationary Systems, Avtom. Telemekh., 1985, no. 11, pp. 26–33.
Gil’, M.I., On a Class of Absolutely Stable Multivariable Systems, Dokl. Akad. Nauk SSSR, 1985, vol. 280, no. 4, pp. 811–815.
Gil’, M.I., On a Class of Absolutely Stable Distributed-parameter Systems, Avtom. Telemekh., 1985, no. 12, pp. 54–59.
Kamenetskii, V.A., Absolute Stability of the Discrete Control Systems with Nonstationary Nonlinearities, Avtom. Telemekh., 1985, no. 8, pp. 172–176.
Leonov, G.A., On a Method of Constructing the Lyapunov Functions, in Ustoichivost’ dvizheniya (Stability of Motion), Novosibirsk: Nauka, 1985, pp. 67–71.
Molchanov, A.P. and Pyatnitskii, E.S., Construction of the Lyapunov Functions Defining the Necessary and Sufficient Conditions for Absolute Stability in the Class of Nonstationary Nonlinearities, in Ustoichivost’ dvizheniya (Stability of Motion), Novosibirsk: Nauka, 1985, pp. 82–88.
Yakubovich, V.A., Absolute Stability in the Given Output of the Nonlinear Systems with Partial Derivatives, in Ustoichivost’ dvizheniya (Motion Stability), Novosibirsk: Nauka, 1985, pp. 22–25.
Yakubovich, V.A., Singular Problem of Optimal Control of the Linear Stationary System with Quadratic Functional, Sib. Mat. Zh., 1985, vol. 26, no. 1, pp. 189–200.
Feng Chubo, Passivity Analysis of Feedback Systems and its Applications, Zidonghua Xuebao/Acta Automatica Sinica, 1985, vol. 11, no. 2, pp. 111–117.
Grujic, L.T., Bucevac, Z., and Ribar, Z., On Necessary and Sufficient Conditions for Absolute Stability of Discrete-time Systems, in Proc. Ninth Triennial World Congr. of IFAC, 1985, vol. 1, pp. 201–205.
Qidi Wu and Djordjevic, M., An Application of Polynomial Positivity to the Absolute Stability Analysis of Nonlinear Systems, Scientia Electrica, 1985, vol. 31, no. 4, pp. 140–152.
1986
Zhuikova, A.G. and Khusainov, D.Ya., Numerical Algorithm to Construct the Optimal Lyapunov Function in the Problems of Absolute Stability, Vest. Kiev. Univ., 1986, no. 5, pp. 73–76.
Zelentsovskii, A.L., Construction of the Lyapunov Functions from the Class of Second-degree Forms for Studying Absolute Stability of the Control Systems with Nonstationary Nonlinear Elements, Avtom. Telemekh., 1986, no. 5, pp. 166–169.
Liberzon, M.R., An Attribute of Absolute Stability of the Nonstationary Systems, Avtom. Telemekh., 1986, no. 2, pp. 39–46.
Molchanov, A.P. and Pyatnitskii, E.S., Lyapunov Functions Defining the Necessary and Sufficient Conditions for Absolute Stability of the Nonlinear Control Systems, I, II, III, Avtom. Telemekh., 1986, no. 3, pp. 63–73; no. 4, pp. 5–15; no. 5, pp. 38–49.
Pakshin, P.V., Algebraic Verification of Absolute Stability, Dokl. Akad. Nauk SSSR, 1986, vol. 290, no. 4–6, pp. 813–815.
Pyatnitskii, E.S. and Skorodinskii, V.I., A Criterion for Absolute Stability of the Nonlinear Fulse Control Systems in the Form of a Numerical Procedure, Avtom. Telemekh., 1986, no. 9, pp. 32–39.
Smolyar, E.I., On Stability in Large of the Nonlinear Systems Meeting the Generalized Hurwitz Conditions, Preprint of Agrophysical Research Inst., All-Union Acad. of Agricultural Sci., Leningrad, 1986, no. 4727.
Smolyar, E.I., On Counterexamples in the Problem of M.A. Aizerman, Preprint of Agrophysical Research Inst., All-Union Acad. of Agricultural Sci., Leningrad, 1986, no. 4728.
Yakubovich, V.A., Linear Quadratic Problem of Optimization and the Frequency Theorem for Periodic Systems, Sib. Mat. Zh., 1986, vol. 27, no. 4, pp. 181–200.
Liao Xiao Xin, The Absolute Stability of Lure direct control systems, in Theory and Appl. Nonlinear Control Syst., Amsterdam: North-Holland, 1986, pp. 513–519.
Resende, P., Kaszkurewicz, E., and Hsu, L., On the Absolute Stability of Multivariable Non-linear Systems Using a Block-tridiagonal State-space Representation, Int. J. Control, 1986, vol. 43, no. 2, pp. 643–655.
1987
Barabanov, N.E., Method of Extending the Circular Criterion for the Pulse Systems of Automatic Control, in Dinamika neodnorodnykh sistem (Dynamics of Nonuniform Systems), Moscow: VNIISI, 1987, vol. 6, pp. 61–68.
Bogatyrev, A.V. and Pyatnitskii, E.S., Construction of the Piecewise-quadratic Lyapunov Functions for the Nonlinear Control Systems, Avtom. Telemekh., 1987, no. 10, pp. 30–38.
Kamenetskii, V.A. and Pyatnitskii, E.S., Gradient Method of Constructing the Lyapunov Functions in the Problems of Absolute Stability, Avtom. Telemekh., 1987, no. 1, pp. 3–12.
Lapin, Yu.N., On Positiveness of the Pulse Functions and Absolute Stability of the Nonlinear Systems in the Hurwitzian Angle, Avtom. Telemekh., 1987, no. 5, pp. 40–47.
Meilakhs, A.M., On Variational Approach to the Problem of Absolute Stability of the Nonstationary Nonlinear Systems, Diff. Uravn., 1987, vol. 23, no. 7, pp. 1464–1466.
Molchanov, A.P., Lyapunov Functions for the Nonlinear Discrete Control Systems, Avtom. Telemekh., 1987, no. 6, pp. 26–35.
Rapoport, L.B., Absolute Stability of the Control Systems with Several Nonlinear Stationary Elements, Avtom. Telemekh., 1987, no. 5, pp. 66–74.
Yunger, I.B., Algebraic Criteria for Absolute Stability of Nonlinear Automatic Control Systems, Avtom. Telemekh., 1987, no. 1, pp. 48–54.
Grujic, L.T. and Petkovski, D.B., Robust Absolutely Stable Lurie Systems, Int. J. Control, 1987, vol. 46, no. 1, pp. 357–368.
Kamenetskiy, V.A. and Pyatnitskiy, E.S., An Iterative Method of Lyapunov Function Construction for Differential Inclusions, Syst. Control Lett., 1987, no. 8, pp. 445–451.
Krishnamurthy, V. and Sastry, G.V.K.R., A New Design Method for Absolute Stability of Nonlinear Systems, J. Inst. of Eng. (India). Electronics & Telecommun. Eng. Division, 1987, vol. 67, pp. 77–80.
1988
Aleksandrov, V.V., Absolute Stability of Simulation Dynamic Systems in First Approximation, Dokl. Akad. Nauk SSSR, 1988, vol. 299, no. 2, pp. 296–301.
Barabanov, N.E., On the Problem of Absolute Stability of the Pulse Automatic Control Systems, Avtom. Telemekh., 1988, no. 8, pp. 28–37.
Barabanov, N.E., On the Kalman Problem, Sib. Mat. Zh., 1988, no. 3, pp. 3–11.
Barabanov, N.E., New Criteria for Absolute Stability of the Automatic Control Systems with One Differentiable Nonlinearity, Dokl. Akad. Nauk SSSR, 1988, vol. 299, no. 3, pp. 570–572.
Barabanov, N.E., On the Lyapunov Index of Discrete Inclusions, Avtom. Telemekh., 1988, no. 5, pp. 17–24.
Levin, A.Yu., A Criterion for Absolute Nonoscillatory Stability of the Equations of the nth Order, Usp. Mat. Nauk, 1988, vol. 43, no. 5, pp. 203, 204.
Liberzon, M.R., On Motional Stability of the Axially Symmetric Rotating Flight Vehicle, Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, 1988, no. 5, pp. 9–14.
Molchanov, A.P., On Equivalence of Two Definitions of Absolute Stability for the Nonstationary Control Systems, Avtom. Telemekh., 1988, no. 10, pp. 187–189.
Rapoport, L.B., Definite Sign of the Quadratic Form for Quadratic Constraints and Absolute Stability of the Nonlinear Control Systems, Dokl. Akad. Nauk SSSR, 1988, vol. 298, no. 4, pp. 822–826.
Yakubovich, V.A., Absolute Stability of the Nonlinear System with Periodic Nonstationary Linear Part, Dokl. Akad. Nauk SSSR, 1988, vol. 298, no. 2, pp. 299–303.
de la Sen, M., Guaranteed Absolute Stability in the Presence of Unmodelled Dynamics, Int. J. Syst. Sci., 1988, vol. 19, no. 1, pp. 77–96.
Grujic, L.T., Algebraic Conditions for Absolute Tracking Control of Lurie Systems, Int. J. Control, 1988, vol. 48, no. 2, pp. 729–754.
Liberzon, M.R., About Absolute Stability of the Follow-up Systems, in Automatika, London: Pergamon, 1988, pp. 1555–1558.
Yakubovich, V.A., Dichotomy and Absolute Stability of Nonlinear Systems with Periodically Nonstationary Linear Part, Syst. Control Lett., 1988, vol. 11, no. 3, pp. 221–228.
1989
Barabanov, N.E., New Frequency Criteria for Absolute Stability and Instability of the Automatic Control Systems with Nonstationary Nonlinearity, Diff. Uravn., 1989, vol. 25, no. 4, pp. 555–563.
Kamenetskii, V.A., Method of Convolution of the Matrix Inequalities and Criteria for Absolute Stability of the Stationary Control Systems, Avtom. Telemekh., 1989, no. 5, pp. 28–39.
Korenevskii, D.G., Absolute Stability of the Continuous and Discrete Nonlinear Stochastic Control Systems. Algebraic Coefficient Criteria, Dokl. Akad. Nauk SSSR, 1989, vol. 306, no. 4–6, pp. 1316–1319.
Liberzon, M.R., Innor Criterion for Absolute Stability of the Nonstationary Systems, Avtom. Telemekh., 1989, no. 5, pp. 40–46.
Liberzon, M.R., Innor Criterion for Absolute Stability of the Nonstationary Control Systems, Dokl. Akad. Nauk SSSR, 1989, vol. 304, no. 5, pp. 1060–1064.
Pakshin, P.V., Algebraic Criterion for Absolute Stability of the Nonlinear Stochastic Systems with Multiplicative White Noise, Sb. tr. VNII sistem. issled. (Proc. Inst. Syst. Res.), 1989, no. 14, pp. 115–123.
Rapoport, L.B., On the Problem of Absolute Stability of the Control Systems with Superposition of the Nonlinear Elements, Avtom. Telemekh., 1989, no. 12, pp. 166–168.
Bar-Kana, I., Absolute Stability and Robust Discrete Adaptive Control, in Proc. IFAC Workshop “Robust Adaptive Control”, 1989, pp. 171–175.
Siljak, D.D., Polytopes of Nonnegative Polynomials, in Proc. 1989 American Control Conf., 1989, vol. 1, pp. 193–199.
1990
Kozyakin, V.S., Absolute Stability of the Discrete Disaligned Systems, Dokl. Akad. Nauk SSSR, 1990, vol. 312, no. 4–6, pp. 1066–1070.
Kozyakin, V.S., Absolute Stability of Systems with Asynchronous Discrete Elements, Avtom. Telemekh., 1990, no. 10, pp. 56–63.
Rapoport, L.G., Boundary of Absolute Stability of the Nonlinear Nonstationary Systems and its Relation with Construction of the Invariant Functions, Avtom. Telemekh., 1990, no. 10, pp. 78–86.
Savkin, A.V., Criterion for Absolute Stability of the Nonlinear Control Systems with Periodic Nonstationary Linear Part, Avtom. Telemekh., 1990, no. 8, pp. 50–55.
Yunger, I.B. and Gerasimov, O.I., Algebraic Criterion for Absolute Stability, Avtomatika, 1990, vol. 23, no. 2, pp. 42–45.
Yakubovich, V.A., Methods of the Absolute Stability Theory in the Problems of Invariance, in Kibernetika i vychislitel’naya tekhnika (Cybernetics and Computer Science), Kiev: Naukova Dumka, 1990, vol. 85, pp. 1–13.
Cheng, Yu., Absolute Stability of Multi-regular Control System in Infinite Hurwitz Angle, Acta Math. Sin., 1990, vol. 33, no. 3, pp. 289–294.
Halanay, A. and Rasvan, V., Absolute Stability of Discrete Systems with Slope Restricted Nonlinearity, Revue Romaine des Sciences Techniques, 1990, vol. 35, no. 1, pp. 101–111.
Liberzon, M.R., Adaptive Control Systems of Electromagnetic Field Influence on Materials, in Evaluation of Adaptive Control Strategies, London: Pergamon, 1990, no. 7, pp. 267–270.
Singh, V., A Generalized Approach for the Absolute Stability of Discrete-time Systems Utilizing the Saturation Nonlinearity Based on Passivity Properties, IEEE Trans. Circuits & Syst., 1990, vol. 37, no. 3, pp. 444–447.
Voronov, A.A., On Absolute Stability Criteria Improvement and Absolute Stability Regions Construction, in Nonlinear Control Syst. Design. Selected Papers from the IFAC Symposium, 1990, pp. 219–223.
Yunger, I.B. and Gerasimov, O.I., New Improved Criteria of Absolute Stability for Nonlinear Dynamical Systems, in Proc. IFAC World Congr., Tallinn, 1990, vol. 6, pp. 31–35.
1991
Aisagaliev, S.A. and Magovin, M.M., On the Theory of Absolute Stability of the Controlled Systems in the Critical Cases, Preprint Kazan. Gos. Tekh. Univ., Kazan, 1991.
Aleksandrova, O.V., Generalized Resonance in the Oscillatory System, Vestn. Mosk. Gos. Univ., Mat. Mekh., 1991, no. 3, pp. 89–92.
Voronov, A.A., On Improving the Criterion for Absolute Stability of Systems with Differentiable Monotone Nonlinearities, in Sb. tr. VNII sistem. issled. (Proc. Inst. Syst. Res.), 1991, no. 14, pp. 22–28.
Kucheev, Z.Sh. and Gerasimov, O.I., Review and Comparative Characterization of the Methods of Numerical Analysis of Absolute Stability of the Nonlinear Automatic Systems, Izv. Leningrad. Elektrotekhn. Inst., 1991, no. 441, pp. 58–62.
Levin, A.G., Decomposition of the Frequency Criteria for Stability of the Multiaggregate Linear Systems, Avtom. Telemekh., 1991, no. 3, pp. 47–59.
Polyak, B.T. and Tsypkin, Ya.Z., Robust Stability of Linear Systems, in Itogi Nauki Tekhn., Tekhn. Kibern., VINITI, 1991, no. 32, pp. 3–31.
Polyak, B.T. and Tsypkin, Ya.Z., Robust Stability under Complex Perturbations of the Parameters, Avtom. Telemekh., 1991, no. 8, pp. 45–55.
Pyatnitskii, E.S. and Rapoport, L.B., Periodic Motions and Criteria for Absolute Stability of Nonlinear Nonstationary Systems, Avtom. Telemekh., 1991, no. 10, pp. 63–73.
Pyatnitskii, E.S. and Rapoport, L.B., Periodic Motions and The Boundary of Asymptotic Stability of the Selector Linear Differential Inclusions, Dokl. Akad. Nauk SSSR, 1991, vol. 321, no. 4, pp. 687–691.
Savkin, A.V., On Absolute Stability of the Nonlinear Control Systems with Nonstationary Linear Part, Avtom. Telemekh., 1991, no. 3, pp. 78–84.
Skorodinskii, V.I., Iterative Methods of Testing the Frequency Criteria for Absolute Stability of the Continuous Control Systems, Avtom. Telemekh., 1991, no. 8, pp. 63–71.
Tsypkin, Ya.Z., Stabilization of the Nonlinear Discrete Systems under Nonparametric Uncertainty, Avtomatika, 1991, vol. 24, no. 4, pp. 3–7.
Fruchter, G., Generalized Zero Sets Location and Absolute Robust Stabilization of Continuous Nonlinear Control Systems, Automatica, 1991, vol. 27, no. 3, pp. 501–512.
Halanay, A. and Rasvan, V., Absolute Stability of Feedback Systems with Several Differentiable Non-linearities, Int. J. Syst. Sci., 1991, vol. 22, no. 10, pp. 1911–1927.
Lee, S. and Meerkov, S.M., Vibrational Feedback Control in the Problem of Absolute Stability, IEEE Trans. Automat. Control, 1991, vol. 36, no. 4, pp. 482–485.
Liao Xiao Xin, Absolute Stability of General Lurie Control Systems, Acta Math. Sci. Engl. Ed., 1991, vol. 11, no. 1, pp. 1–12.
Tesi, A. and Vicino, A., Robust Absolute Stability of Lur’e Control Systems in Parameter Space, Avtomatika, 1991, vol. 27, no. 1, pp. 147–151.
Xiao Shuxian, On Lur’e Functions for Nonlinear Systems, Control Theory Appl., 1991, vol. 8, no. 3, pp. 268–274.
1992
Gerasimov, O.I. and Yunger, I.B., Frequency Algebraic Analysis of Absolute Stability of the Nonlinear Automatic Control Systems, Izv. Ross. Akad. Nauk, Tekh. Kibern., 1992, no. 1, pp. 213–217.
Levin, A.G., Precise Estimation of the Oscillation Index of the Class of Multivariable Linear Systems, Avtom. Telemekh., 1992, no. 9, pp. 65–72.
Molchanov, A.P. and Morozov, M.V., Lyapunov Functions for the Nonlinear Nonstationary Discrete Control Systems with Periodic Linear Part, Avtom. Telemekh., 1992, no. 10, pp. 37–45.
Morozov, M.V., On Equivalence of Two Definitions of Absolute Stability of the Nonlinear NOnstationary Control Systems with Periodic Linear Part, Avtom. Telemekh., 1992, no. 8, pp. 46–53.
Savkin, A.V., Nonstationary Analog of the Kalman-Yakubovich Lemma and its Application in the System Theory, Avtomatika, 1992, vol. 25, no. 3, pp. 47–51.
Spasskii, R.A., On One Problem of FV Stabilization, in Tr. 26 chtenii, posvyashch. razrab. nauch. naslediya i razvitiyu idei K.E. Tsiolkovskogo (Proc. 26th Readings on Development of Scientific Heritage and Extension of the Ideas of K.E. Tsiolkovskii), Moscow, 1992, pp. 107–109.
Churilov, A.N., Frequency Criterion for Stability of the Nonlinear Pulse Systems with Even Pulsation Law, Avtom. Telemekh., 1992, no. 4, pp. 93–100.
Savkin, A.V., The Kalman-Yakubovich lemma for Non-stationary systems and its Applications, Int. J. Adaptive Control & Signal Proc., 1992, vol. 6, no. 3, pp. 253–257.
1993
Aleksandrov, V.V., Krasil’nikova, I.E., and Torres, A., Absolute Stability in One-dimensional Oscillatory Systems, in Zadacha Bulgakova o maksimal’nom otklonenii i ee primenenie (Bulgakov Problem of Maximal Deviation and its Application), Moscow: Mosk. Gos. Univ., 1993, pp. 48–57.
Gerasimov, O.I. and Yunger, I.B., Matrix Criterion for Absolute Stability of the Pulse Automatic Control systems, Avtom. Telemekh., 1993, no. 2, pp. 134–139.
Zhermolenko, V.N., Khing Korton, R., and Gonsales, G., Absolute Stability of Two-dimensional Systems, in Zadacha Bulgakova o maksimal’nom otklonenii i ee primenenie (Bulgakov Problem of Maximal Deviation and its Application), Moscow: Mosk. Gos. Univ., 1993, pp. 57–80.
Rapoport, L.B., Antiperiodic Motions and Algebraic Criterion for Absolute Stability of the Nonlinear Nonstationary Systems in the Three-dimensional Case, Avtom. Telemekh., 1993, no. 7, pp. 38–54.
Savkin, A.V., An Analog of the Frequency Theorem for the Nonstationary Systems, Izv. Ross. Akad. Nauk, Tekh. Kibern., 1993, no. 2, pp. 26–30.
Beklemishev, N.N. and Liberzon, M.R., The Use of Inner Method in Stability Analysis of Control Systems for Special Technological Processes, in Proc. Int. Symp. Fundamentals of Discrete-Time Systems, New Mexico: TSI Press, 1993, pp. 189–194.
Halanay, A. and Ionescu, V., Generalized Discrete-time Popov-Yakubovich Theory, Syst. Control Lett., 1993, no. 1, pp. 1–6.
How, J.P., Haddad, W.M., and Hall, S.R., Robust Control Synthesis Examples with Real Parameter Uncertainty Using the Popov Criterion, in Proc. Am. Control Conf., 1993, vol. 2, pp. 1090–1095.
How, J.P. and Hall, S.R., Connections between the Popov Stability Criterion and Bounds for Real Parameter Uncertainty, in Proc. Am. Control Conf., 1993, vol. 2, pp. 1084–1089.
Liao Fucheng, Absolute Stability for a Class of Indirect Control Systems, Acta Sci. Natur. Univ. Neimenggu, 1993, vol. 24, no. 3, pp. 235–241.
Liberzon, M.R., Inner Indication of Absolute Stability for Discrete Systems, in Proc. Int. Symp. Fundamentals of Discrete-Time Syst., New Mexico: TSI Press, 1993, pp. 333–338.
Megretski, A., Necessary and Sufficient Conditions of Stability: A Multiloop Generalization of the Circle Criterion, IEEE Trans. Automat. Control, 1993, vol. 38, no. 5, pp. 753–756.
Minyue, F. and Tsypkin, Ya.Z., Modified Mikhailov Plots for Robust Absolute Stability with Nonparametric Perturbations and Uncertain Nonlinearity, Int. J. Control, 1993, vol. 58, no. 4, pp. 925–932.
Nishimura, T., Mori, T., Kuroe, Y., and Kokame, H., On Application of Popov’s Theorem for Lur’e Systems with Interval Plants, Trans. Inst. Syst., 1993, vol. 6, no. 4, pp. 165–170.
Rongdong Wang, Symbolic Computation Approach for Absolute Stability, Int. J. Control, 1993, vol. 58, no. 2, pp. 495–502.
Tsypkin, Ya.Z. and Polyak, B.T., Robust Absolute Stability of Continuous Systems, Int. J. Robust & Nonlinear Control, 1993, vol. 3, no. 3, pp. 231–239.
Worland, P.B., Parallel Methods for ODEs with Improved Absolute Stability Boundaries, J. Parallel & Distributed Comput., 1993, vol. 18, no. 1, pp. 25–32.
Yuanji Cheng and Lina Wang, On the Absolute Stability of Multi-nonlinear Control Systems in the Critical Cases, IMA J. Math. Control & Inform., 1993, vol. 10, no. 1, pp. 1–10.
Yunger, I.B. and Gerasimov, O.I., Algebraic Analysis of Absolute Stability for Uncertain Dynamical Systems with Nonlinear Time-varying Properties, Automatica, 1993, vol. 29, no. 3, pp. 763–766.
Zhao Keyou, An Extended Popov Criterion for a Class of Uncertain Systems, Control Theory & Appl., 1993, vol. 10, no. 1, pp. 108–112.
1994
Aleksandrova, O.V., On Estimation of Oscillations of Permanently Perturbed Systems, Vestn. Mosk. Gos. Univ., Mat. Mekh., 1994, no. 5, pp. 54–58.
D’yachenko, I.V., Molchanov, A.P., and Pyatnitskii, E.C., Numerical Method of Construction of the Lyapunov Functions and Computer-aided Analysis of Stability of the Nonlinear Dynamic Systems, Avtom. Telemekh., 1994, no. 4, pp. 23–38.
Alexandrov, V.V., Liberzon, M.R., and Rozov, N.Kh., On the Absolute Stability of Monomeasurable Control Systems, in Syst. Networks: Math. Theory Appl., Berlin: Academie Verlag, 1994, vol. 2, pp. 39–41.
Brusin, V.A. and Ugrinovsky, V.A., Absolute Stability Approach to Stochastic Stability of Non-linear Infinite Dimensional Feedback Evolution Equations, in Proc. IFAC World Congress, 1994, pp. 59–62.
Gil, M.I., Class of Absolutely Stable Multivariable Systems, Int. J. Syst. Sci., 1994, vol. 25, no. 3, pp. 613–617.
Haddad, W.M., How, J.P., Hall, S.R., and Bernstein, D.S., Extensions of Mixed-mu Bounds to Monotonic and Odd Monotonic Nonlinearities Using Absolute Stability Theory, Int. J. Control, 1994, vol. 60, no. 5, pp. 905–951.
How, J.P., Hall, S.R., and Haddad, W.M., Robust Controllers for the Middeck Active Control Experiment Using Popov Controller Synthesis, IEEE Trans. Control Syst. Technology, 1994, vol. 2, no. 2, pp. 73–87.
Liberzon, M.R., Adaptive Control Systems for New Technological Processes, in Proc. Int. Aerospace Congr. IAC’94, Moscow, 1994, vol. 2, pp. 163–167.
Liberzon, M.R., Control Systems for Special Technological Processes of Metal Production, in Proc. Int. Symp. Space Technology Sci., Yokohama, 1994.
Liberzon, M.R., Inner Approach for the Absolute Stability of Time-lag Dynamical Systems, in Proc. Int. Congress. Mathematicians ICM’94, Zurich, 1994.
Liberzon, M.R., Stability of Rolling Mill Processes, in Proc. IFAC Conf. on ISE, Baden-Baden, 1994, pp. 29, 30.
Nishimura, T., Mori, T., Kuroe, Y., and Kokame, H., Robust Absolute Stability of Lur’e Systems with Interval Plants and General Sector-type Nonlinearities, Trans. Inst. Electronics & Commun. Eng. Japan, 1994, vol. 114-C, no. 2, pp. 239–244.
Premarante, K. and Jury, E.I., Discrete-time Positive-real Lemma Revisited: The Discrete-time Counter Part of the Kalman-Yakubovitch Lemma, IEEE Trans. Circuits & Syst., 1994, vol. 41, no. 11, pp. 747–750.
Zhang Jiye and Shu Zhong-zhou, Necessary and Sufficient Criteria for Absolute Stability of the Direct Control System, Appl. Math. & Mechanics, 1994, vol. 15, no. 3, pp. 245–251.
1995
Molchanov, A.P. and Morozov, M.V., Robust Absolute Stability of the Nonstationary Discrete Control Systems with Periodic Constraints, Avtom. Telemekh., 1995, no. 10, pp. 93–100.
Rapoport, L.B., Antiperiodic Motions and the Algebraic Criterion for Asymptotic Stability of the Selector Linear Differential Inclusions in the Two-dimensional Case, Avtom. Telemekh., 1995, no. 1, pp. 56–63.
Churilova, M.Yu., An Analog of the Circular Criterion for Absolute Stability for Variable-delay Systems, Avtom. Telemekh., 1995, no. 2, pp. 52–56.
Brusin, V.A. and Ugrinovskii, V.A., Absolute Stability Approach to Stochastic Stability of Infinite-dimensional Nonlinear Systems, Automatica, 1995, vol. 31, no. 10, pp. 1453–1458.
Feng-Hsiag Hsiao, Jer-Guang Hsieh, and Jaion-Shea Chang, New Algebraic Criteria for Absolute Stability of Nonlinear Systems, Int. J. Robust & Nonlinear Control, 1995, vol. 5, no. 6, pp. 591–607.
Gelig, A.Kh. and Churilov, A.N., Frequency-domain Criteria for Absolute Stability of Nonlinear Systems with Various Types of Pulse Modulation, in Proc. Eur. Control Conf., 1995, vol. 3, pp. 2251–2255.
Kaiqi Xiong, Necessary and Sufficient Conditions for the Existence of a G-type Lyapunov Function, Automatica, 1995, vol. 31, no. 5, pp. 787–791.
Liberzon, M.r., Stability of Control Systems for New Technological Processes of Special Metal Production, in Proc. Int. Congr. Industrial Appl. Math., Hamburg 1995, pp. 167–171.
Megretski, A., Combining L1 and L2 Methods in the Robust Stability and Performance Analysis of Nonlinear Systems, in Proc. IEEE Conf. Decision and Control, 1995, vol. 3, pp. 3176–3781.
Savkin, A.V. and Petersen, I.R., A Method for Robust Stabilization Related to the Popov Stability Criterion, Int. J. Control, 1995, vol. 62, no. 5, pp. 1105–1115.
Wada, T., Ikeda, M., Ohta, Y., and Siljak, D.D., Parametric Absolute Stability of Multivariable Lur’e Systems—a Popov-type Condition and Application of Polygoninterval Arithmetic, Trans. Soc. Instrument Control Eng., 1995, vol. 31, no. 9, pp. 1329–1335.
Zhang Jiye, Necessary and Sufficient Conditions for the Absolute Stability of Discrete Type Lurie Control System, Appl. Math. & Mechanics, 1995, vol. 16, no. 10, pp. 995–1001.
1996
Badmaeva, S.V. and Barabanov, N.E., Strengthening of the Criteria for Absolute Stability of the Automatic Control Systems with Several Nonstationary Nonlinearities, Izv. Ross. Akad. Nauk, Teor. Sist. Upravlen., 1996, no. 1, pp. 5–9.
Barkin, A.I., On Two Criteria for Absolute Stability of Discrete Systems, Avtom. Telemekh., 1996, no. 1, pp. 21–26.
Malikov, A.I., Absolute Stability of the Nonlinear Controlled Systems with Random Variations of their Structure, Izv. Ross. Akad. Nauk, Teor. Sist. Upravlen., 1996, no. 3, pp. 19–30.
How, J.P., Collins, E.G., and Haddad, W.M., Optimal Popov Controller Analysis and Synthesis for Systems with Real Parameter Uncertainties, IEEE Trans. Control Syst. Technology, 1996, vol. 4, no. 2, pp. 200–207.
Kaiqi Xiong, Necessary and Sufficient Conditions for the Existence of a Lyapunov Function with ‘a Quadratic Form Plus an Integral Term,’ Int. J. Control, 1996, vol. 64, no. 4, pp. 707–719.
Liberzon, M.R., Improvement of Plasticity and Other Properties of Metals by Electromagnetic Field, in Proc. 19th Int. Congr. Theoretical Appl. Mechanics, Kyoto, 1996.
Pyatnitsky, E.S. and Rapoport, L.B., Criteria of Asymptotic Stability of Differential Inclusions and Periodic Motions of Time-varying Nonlinear Control Systems, IEEE Trans. Circuits & Syst., 1996, vol. 43, no. 3, pp. 219–229.
Rasvan, V., Stabilization and Decoupling Control Applied in Vehicle Dynamics, in Proc. 1995 IFAC Workshop Control Appl. Optim. A Postprint Volume, London: Pergamon, 1996, pp. 97–102.
Savkin, A.V. and Evans, R.J., Robust Output Feedback Stabilizability via Controller Switching, in Proc. IEEE Conf. Decision Control, 1996, vol. 3, pp. 2654–2658.
1997
Molchanov, A.P. and Morozov, M.V., Sufficient Conditions for Robust Stability of the Linear Nonstationary Control Systems with Periodic Constraints, Avtom. Telemekh., 1997, no. 1, pp. 100–107.
Molchanov, A.P. and Morozov, M.V., Algorithms for Analysis of Robust Stability of the Linear Nonstationary Control Systems with Periodic Constraints, Avtom. Telemekh., 1997, no. 5, pp. 100–111.
Curran, P.F., Suykens, J.A.K., and Chua, L.O., Absolute Stability Theory and Master-Slave Synchronization, Int. J. Bifurcat. & Chaos Appl. Sci. & Eng., 1997, vol. 7, no. 12, pp. 2891–2896.
Grujic, L.T., New Lyapunov Methodology: Absolute Stability of Lurie-Postnikov System, in Proc. IFAC Conf. Control Industrial Syst. ‘Control for the Future of the Youth,’ 1997, vol. 1, pp. 409–414.
Liberzon, M.R., New Technological Process for Preparation of Sandwich from Metals, in Proc. EUROMECH 360 Symp., Saint Etienne, 1997, pp. 135–137.
Moheimani, S.O.R., Savkin, A.V., and Petersen, I.R., Minimax Optimal Control of Discrete-time Uncertain Systems with Structured Uncertainty, Dynamics & Control, 1997, vol. 7, no. 1, pp. 5–24.
Pakshin, P.V., Robust Absolute Stability of Jumping Stochastic Systems, in Proc. IFAC Symp. Robust Control Design. (ROCOND’97), 1997, pp. 159–164.
Rapoport, L.B., New Frequency Criteria for Analysis of Multivariable Lure Systems, in Proc. IFAC World Congr., 1997, pp. 25–30.
Ugrinovsky, V.A. and Petersen, I.R., Absolute Stabilization and Minimax Optimal Control of Uncertain Systems with Stochastic Uncertainty, in Proc IFAC Symp. on Robust Control Design (ROCOND’97), 1997, pp. 125–130.
Wada, T., Ikeda, M., Ohta, Y., and Siljak, D.D., Parametric Absolute Stability of Multivariable Lure Systems: An LMI Condition and Application to Polytopic Systems, in Proc. IFAC World Cong., 1997, pp. 19–24.
1998
Bliman, P.A. and Krasnosel’skii, M.A., Popov Criterion in the Problem of Forced Oscillations in the Control Systems, Avtom. Telemekh., 1996, no. 4, pp. 3–14.
Kaizer, K. and Korenevskii, D.G., Algebraic Coefficient Attributes of Absolute Stability of the Linear Difference Systems with Continuous Time and Delay, Avtom. Telemekh., 1998, no. 1, pp. 22–27.
Liberzon, M.R., Extension of the Innor Method of the Absolute Stability Theory to the Delay Systems, in Nauchn. tr. Mosk. aviats. tekhnol. in-ta—Ross. gos. tekhnol. un-ta im. K.E. Tsiolkovskogo (Proc. Moscow Aviation Technol. Inst.—K.E. Tsiolkovskii Russian State Technol Univ.), Moscow: LATMES, 1998, vol. 1 (73), pp. 336–340.
Tseligorov, N.A., Methodology of Grapho-analitical Study of Absolute Stability of MIMO Nonlinear Pulse Automatic Systems, Izv. Vuzov, Elektromekh., 1998, no. 4, pp. 72–75.
Yakubovich, V.A., Quadratic Criterion for Absolute Stability, Dokl. Ross. Akad. Nauk, 1998, vol. 361, no. 5, pp. 608–611.
Bucci, F., Absolute Stability of Feedback Systems in Hilbert Spaces, Izv. Vuzov, Elektromekh., 1998, pp. 24–39.
Chen, Ya., Chen, Sh., and Liu, J., Frequency Theorem (Kalman-Yakubovich lemma) in Control Theory, Control Theory & Appl., 1998, vol. 15, no. 4, pp. 477–488.
Curran, P.F. An Overview of Absolute Stability Theory, in Proc. Int Specialist Workshop on Nonlinear Dynamics of Electronic Syst., Budapest, 1998, pp. 63–72.
de la Sen, M. and Jugo, J., Absolute Stability and HyperStability of a Class of Hereditary Systems, Informatica (Ljubljana), 1998, vol. 9, no. 2, pp. 195–208.
Hagiwara, T., Kuroda, G., and Araki, M., Popov-type Criterion for Stability of Nonlinear Sampled-data Systems, Autornatica, 1998, vol. 34, no. 6, pp. 671–682.
Liberzon, M.R., Inners and Absolute Stability of Time-lag Systems, in Proc. Int. Congr. Mathematicians, Berlin, 1998.
Poogyeon Park and Sang Woo Kim, A Revisited Tsypkin Criterion for Discrete-time Nonlinear Lur’e Systems with Monotonic Sector-restrictions, Automatica, 1998, vol. 34, no. 11, pp. 1417–1420.
Savkin, A.V. and Petersen, I.R., Robust Stabilization of Discrete-time Uncertain Nonlinear Systems, J. Optim. Theory & Appl., 1998, vol. 96, no. 1, pp. 87–107.
Wada, T., Ikeda, M., Ohta, Y., and Siljak, D.D., Parametric Absolute Stability of Lur’e Systems, IEEE Trans. Automat. Control, 1998, vol. 43, no. 11, pp. 1649–1653.
1999
Jury, E.I., Premaratne, K., and Ekanaiake, M.M., Robust Absolute Stability of Discrete Systems, Avtom. Telemekh., 1999, no. 3, pp. 97–118.
Dudnikov, E.E., Stabilization of One-layer Neural Feedback Networks, Neirokomp’yutery: Razrabotka, Primenenie, 1999, no. 1, pp. 38–46.
Dudnikov, E.E. and Rybashov, M.V., On Absolute Stability of a Class of Neural Feedback Networks, Avtom. Telemekh., 1999, no. 12, pp. 33–40.
Kogan, M.M., Minimax Approach to the Design of Absolute Stabilizing Controllers for the Nonlinear Lur’s Systems, Avtom. Telemekh., 1999, no. 5, pp. 78–91.
Tseligorov, N.A., Absolute Stability Conditions for the Interval Systems, Izv. Ross. Akad. Nauk, Teor. Sist. Upravlen., 1999, no. 2, pp. 10–13.
Bliman, P.A., Extension of Popov Criterion to Time-varying Nonlinearities: LMI, Frequency and Graphic Conditions, Stability and Stabilization of Nonlinear Systems, London: Springer, 1999, no. 246, pp. 95–114.
Guo Lei, Zang Minglei, and Feng Chunbo. Nonlinear Controller Design for Absolute Stabilization Control Problems, Control Theory & Appl., 1999, vol. 16, no. 6, pp. 788–792.
Haddad, W.M., Chellaboina, V.S., and Kablar, N.A., Nonlinear Impulsive Dynamical Systems. I. Stability and dissipativity, in Proc. IEEE Conf. Decision and Control, 1999, vol. 5, pp. 4404–4422.
Liberzon, M.R., On the Stability of Controlled Flight of an Axisymmetric Rotating Vehicle with Incomplete Model Information, in Proc. Am. Control Conf., San Diego, 1999, vol. 5, pp. 3530–3533.
Rapoport, L.B., Estimation of an Attraction Domain for Multivariable Lur’e Systems using Looseless Extension of the S-procedure, in Proc. Am. Control Conf., San Diego, 1999, vol. 4, pp. 2395, 2396.
Zhang Jiye, Wu Pingbo, and Zeng Jing, The Absolute Stability of Several Classes of Nonlinear Control Systems, J. Southwest Jiaotong University (English Edition), 1999, vol. 7, no. 1, pp. 79–86.
2000
Yakubovich, V.A. and Yakubovich, D.V., A Local Analog of the Popov Frequency Criterion for Absolute Stability of the Nonlinear System, Dokl. Ross. Akad. Nauk, 2000, vol. 371, no. 4, pp. 462–465.
Banos, A. and Barreiro, A., Stability of Non-linear QFT Designs Based on Robust Absolute Stability Criteria, Int. J. Control, 2000, vol. 73, no. 1, pp. 74–88.
Bliman, P.-A., Extension of Popov Absolute Stability Criterion to Non-autonomous Systems with Delays, Int. J. Control, 2000, vol. 73, no. 15, pp. 1349–1361.
Brockett, R.W. and Liberzon, D.M., Quantized Feedback Stabilization of Linear Systems, IEEE Trans. Automat. Control, 2000, vol. 45, no. 7, pp. 1279–1289.
Diamond, P. and Opoitsev, V., Absolute Stability of Positive Systems with Differential Constraints, Int. J. Control, 2000, vol. 73, no. 3, pp. 210–218.
Liberzon, M.R. and Matveev, A.E., Calculations Method of Absolute Stability Analysis of Dynamic Systems with Use of Inner Approach, Proc. Int. Conf. SCAN2000, Karlsruhe, 2000, pp. 72, 73.
Logemann, H. and Curtain, R.F., Absolute Stability Results for Well-posed Infinite-dimensional Systems with Applications to Low-gain Integral Control, ESAIM Control. Optim. Calculus of Variations, 2000, no. 5, pp. 395–424.
Polanski, A., On Absolute Stability Analysis by Polyhedral Lyapunov Functions, Automatica, 2000, vol. 36, no. 4, pp. 573–578.
Wada, T., Ikeda, M., Ohta, Y., and Siljak, D.D., Parametric Absolute Stability of Multivariable Lur’e Systems, Automatica, 2000, vol. 36, no. 9, pp. 1365–1372.
Yakubovich, V.A., Necessity in Quadratic Criterion for Absolute Stability, Int. J. Robust and Nonlinear Control, 2000, vol. 10, no. 11, pp. 889–907.
Yang Bin and Chen Mianyun, New Criteria on the Absolute Robust Stability of Lurie Control Systems, J. Huazhong (Central China) University of Science & Technology, 2000, vol. 28, no. 2, pp. 5–7.
2001
Zhermolenko, V.N., Robust Stabilization of the Parametrically Perturbed Systems, Avtom. Telemekh., 2001, no. 2, pp. 122–135.
Bliman, P.-A., Lyapunov-Krasovskii Functionals and Frequency Domain: Delay-independent Absolute Stability Criteria for Delay Systems, Int. J. Robust and Nonlinear Control, 2001, vol. 11, no. 8, pp. 771–788.
Brogliato, B., Absolute Stability and the Lagrange-Dirichlet Theorem with Monotone Multivalued Mappings, in Proc. IEEE Conf. Decision and Control, 2001, vol. 1, pp. 27–32.
Chu, T., Huang, L., and Wang, L., Absolute Stability and Guaranteed Domain of Attraction for MIMO Discrete-time Lur’e Systems, in Proc. IEEE Conf. Decision and Control, 2001, vol. 2, pp. 1711–1716.
Chu, T., Huang, L., and Wang, L., Guaranteed Absolute Stability and Robustness of a Class of Delay Systems with Local Sector Nonlinearities via Piecewise Linear Lyapunov Function, in Proc. Am. Control Conf., 2001, vol. 6, pp. 4212–4217.
Gan, Z., The Robust Absolute Stability of Discrete-time Interval Lurie System, in Proc. IEEE Conf. Decision and Control, 2001, vol. 2, pp. 1991, 1992.
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Original Russian Text © M.R. Liberzon, 2006, published in Avtomatika i Telemekhanika, 2006, No. 10, pp. 86–119.
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Liberzon, M.R. Essays on the absolute stability theory. Autom Remote Control 67, 1610–1644 (2006). https://doi.org/10.1134/S0005117906100043
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DOI: https://doi.org/10.1134/S0005117906100043