Abstract
Consideration was given to the systems of H ∞-suboptimal and modal control and the causes of their small phase and magnitude margins.
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Polyak, B.T. and Shcherbakov, P.S., Robastnaya ustoichivost’ i upravlenie (Robust Stability and Control), Moscow: Nauka, 2002.
Bhattcharyya, S.P., Chapellat, H., and Keel, L.H., Robust Control. The Parametric Approach, New York: Prentice Hall, 1995.
Letov, A.M., Analytical Design of Controllers. I–IV, Avtom. Telemekh., 1960, no. 4, pp. 436–441; no. 5, pp. 561–568; no. 6, pp. 661–665; 1961, no. 4, pp. 425–435.
Kalman, R.E., Contributions to the Theory of Optimal Control, Bullet Soc. Mat. Mech., 1960, vol. 5, no. 1, pp. 102–119.
Anderson, B.D.O. and Moor, J.B., Linear System Optimization with Prescribed Degree of Stability, Proc. Inst. Eng., 1969, vol. 116, no. 2, pp. 100–106.
Aleksandrov, A.G., Frequency Characteristics of the Optimal Linear Control Systems, Avtom. Telemekh., 1969, no. 9, pp. 176–181.
Aleksandrov, A.G., Degree of Robustness of the System with Restorers of Phase Variables, in “Analiticheskie metody sinteza kontrollerov” (Analytical Methods of Controller Design), Saratov: Sarat. Politekhn. Inst., 1977, no. 2, pp. 105–118.
Doyle, J.C., Guaranteed Margins for LQG-regulators, IEEE Trans. Automat. Control, 1978, vol. AC-23, no. 4, pp. 756–757.
Doyle, J.C. and Stein, G., Robustness with Observes, IEEE Trans. Automat. Control, 1979, vol. 24, no. 1, pp. 607–611.
Aleksandrov, A.G., Analytical Design of the Controller Transfer Matrices by the Frequency Performance Criteria. I, Avtom. Telemekh., 1971, no. 12, pp. 12–20.
Safonov, M.G. and Athans, M., Gain and Phase Margin for Multi-loop LQG Regulators, IEEE Trans. Automat. Control, 1977, vol. AC-22, no. 2, pp. 173–179.
Chestnov, V.N., On Possible Instability of the Controlled Systems and Design of Controllers with Regard for the Parametric Perturbations, in “Analiticheskie metody sinteza kontrollerov” (Analytical Methods of Controller Design), Saratov: Sarat. Politekhn. Inst., 1984, pp. 26–35.
Aleksandrov, A.G., Degree of Robustness and Frequency Performance of Automatic Control, in “Analiticheskie metody sinteza kontrollerov” (Analytical Methods of Controller Design), Saratov: Sarat. Politekhn. Inst., 1976, no. 1, pp. 14–26.
Doyle, J.C., Glover, K., Khagonekar, P.P., and Franis, B.A., State-space Solution to Standard H 2 and H ∞ Control Problem, IEEE Trans. Automat. Control, 1989, vol. 34, no. 8, pp. 831–846.
Aleksandrov, A.G., Robustness Criteria for the Nonstationary Control Systems, in “Analiticheskie metody sinteza kontrollerov” (Analytical Methods of Controller Design), Saratov: Sarat. Politekhn. Inst., 1980, pp. 3–14.
Aleksandrov, A.G., Analytical Design of the Controller Transfer Matrices by the Frequency Performance Criteria. II, Avtom. Telemekh., 1972, no. 2, pp. 17–29.
Lhentomaki, N.A., Sandell, N.R., and Athans, M., Robustness Results in Linear-quadratic Gaussian Based Multivariable Control Design, IEEE Trans. Automat. Control, 1981, vol. 26, no. 1, pp. 75–92.
Aleksandrov, A.G. and Khlebalin, N.A., Analytical Design of Controllers under Incomplete Information about the Parameters of the Controlled Plant, in “Analiticheskie metody sinteza kontrollerov” (Analytical Methods of Controller Design), Saratov: Sarat. Politekhn. Inst., 1981, pp. 138–147.
Alexandrov, A.G., Guaranteed Stabilized Plant, in Eur. Control Conf. ECC’03, Cambridge, 2003.
Chestnov, V.N., Synthesis of Controllers for Multivariate Systems with a Given Radius of Stability Margin by the H ∞-Optimization Method, Avtom. Telemekh., 1999, no. 7, pp. 100–109.
Agafonov, P.A. and Chestnov, V.N., Simultaneous Maintenance of the Input and Output Stability Margins of the Multivariable Plant Based of the H ∞ Approach, Avtom. Telemekh., 2004, no. 9, pp. 110–119.
Keel, L. and Bhattacharyya, S.P., Robust, Fragile, or Optimal?, IEEE Trans. Automat. Control, 1997, vol. 42, no. 8, pp. 1098–1105.
Doyle, J.C., Franis, B.A., and Tannenbaum, A.R., Feedback Control Theory, New York: MacMillan, 1992.
Anderson, B.D.O., From Youla-Kucera to Identification, Adaptive and Nonlinear Control, in 13 World Congr. of IFAC, 1996, San Francisco, USA, pp. 39–59.
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Original Russian Text © A.G. Aleksandrov, 2007, published in Avtomatika i Telemekhanika, 2007, No. 8, pp. 4–17.
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Aleksandrov, A.G. Stability margins of the systems of optimal and modal control. Autom Remote Control 68, 1296–1308 (2007). https://doi.org/10.1134/S0005117907080024
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DOI: https://doi.org/10.1134/S0005117907080024