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Reduction of Stability Study of Nonlinear Dynamic Systems by the Second Lyapunov Method

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Abstract

Consideration was given to the conditions for reduction of stability study by the second Lyapunov method of the original nonlinear autonomous dynamic system obeying a system of arbitrary-order ordinary differential equations to stability study of a simpler (abridged) dynamic system using the same method. For a wide class of original nonlinear dynamic systems, sufficient reduction conditions for asymptotic stability and instability were presented.

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REFERENCES

  1. Lyapunov, A.M., Obshchaya zadacha ob ustoichivosti dvizheniya (General Problem of Motion Stability), Moscow: ONTI, 1935.

    Google Scholar 

  2. Chetaev, N.G., Ustoichivost' dvizheniya (Motion Stability), Moscow: Nauka, 1965.

    Google Scholar 

  3. Krasovskii, N.N., Nekotorye zadachi teorii ustoichivosti dvizheniya (Some Problems of Motion Stability Theory), Moscow: Fizmatgiz, 1959.

    Google Scholar 

  4. Malkin, I.G., Teoriya ustoichivosti dvizheniya (Theory of Motion Stability), Moscow: Nauka, 1966.

    Google Scholar 

  5. Zubov, V.I., Ustoichivost' dvizheniya (Motion Stability), Moscow: Vysshaya Shkola, 1973.

    Google Scholar 

  6. Kurosh, A.G., Kurs vysshei algebry (Course of Higher Algebra), Moscow: Fizmatgiz, 1962.

    Google Scholar 

  7. Golovina, L.I., Vysshaya algebra i nekotorye ee prilozheniya (Higher Algebra and Some of Its Applications), Moscow: Nauka, 1985.

    Google Scholar 

  8. Shilov, G.E., Matematicheskii analiz (spetsial'nyi kurs) (Mathematical Analysis (Special course)), Moscow: Fizmatgiz, 1961.

    Google Scholar 

  9. Shilov, G.E., Matematicheskii analiz (funktsii neskol'kikh veshchestvennykh peremennykh) (Mathematical Analysis (Function of Several Real Variables)), Moscow: Nauka, 1972.

    Google Scholar 

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Authors and Affiliations

  1. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia

    V. P. Zhukov

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  1. V. P. Zhukov
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Translated from Avtomatika i Telemekhanika, No. 12, 2005, pp. 51–64.

Original Russian Text Copyright © 2005 by Zhukov.

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Zhukov, V.P. Reduction of Stability Study of Nonlinear Dynamic Systems by the Second Lyapunov Method. Autom Remote Control 66, 1916–1928 (2005). https://doi.org/10.1007/s10513-005-0224-9

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  • DOI: https://doi.org/10.1007/s10513-005-0224-9

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