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Technical stability of autonomous control systems with variable structure

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Abstract

We obtain conditions for the technical stability of autonomous dynamical systems with discontinuous control with respect to a given measure.

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References

  1. E. A. Barbashin,Introduction to Stability Theory [in Russian], Nauka, Moscow (1967).

    Google Scholar 

  2. S. V. Emel’yanov, V. I. Utkin, V. A. Taran, N. E. Kostileva, A. I. Shubladze, V. B. Ezerov, and E. N. Dubrovskii,Theory of Systems with Variable Structure [in Russian], Nauka, Moscow (1970).

    MATH  Google Scholar 

  3. V. I. Utkin,Sliding Modes in Problems of Optimization and Control [in Russian], Nauka, Moscow (1989).

    Google Scholar 

  4. G. I. Lozgachev, “On the construction of Lyapunov functions for systems with variable structure,”Avtomat. Telemekh., No. 8, 161–162 (1972).

    Google Scholar 

  5. V. I. Zubov,Lectures on Control Theory [in Russian], Nauka, Moscow (1975).

    Google Scholar 

  6. L. T. Ashchepkov,Optimal Control over Discontinuous Systems [in Russian], Nauka, Novosibirsk (1987).

    Google Scholar 

  7. A. S. Meshchanov, “Application of the method of Lyapunov functions to the construction of discontinuous controls,” in:Method of Lyapunov Functions in the Dynamics of Nonlinear Svstems [in Russian], Nauka, Novosibirsk (1983), pp. 102–110.

    Google Scholar 

  8. A. F. Filippov,Differential Equations with Discontinuous Right-Hand Side [in Russian], Nauka, Moscow (1985).

    MATH  Google Scholar 

  9. M. M. Khapaev, “Controllability conditions for singularly perturbed systems with singular controls,”Dokl. Akad. Nauk SSSR,320, No. 2, 300–302 (1991).

    Google Scholar 

  10. G. I. Kamenkov, “Stability on a finite time interval,”Prikl. Mat. Mekh.,17, Issue 5, 529–540 (1953).

    MATH  MathSciNet  Google Scholar 

  11. N. F. Kirichenko,Specific Problems of Stability and Controllability of Motion [in Russian], Kiev University, Kiev (1972).

    Google Scholar 

  12. F. G. Garashchenko and N. F. Kirichenko, “Investigation of problems of practical stability and stabilization of motion,”Izv. Akad. Nauk SSSR. Mekh. Tverd. Tela, No. 6, 15–24 (1975).

  13. F. G. Garashchenko, “Specific problems of dynamical stability and their applications,”Vychisl. Prikl. Mat., Issue 46, 106–112 (1982).

    Google Scholar 

  14. V. M. Kuntsevich and M. M. Lychak,Synthesis of Systems of Automatic Control with the Use of Lyapunov Functions [in Russian], Nauka, Moscow (1977).

    Google Scholar 

  15. K. S. Matviichuk, “Technical stability of controlled processes with lumped parameters,”Prikl. Mekh.,33, No. 2, 74–79 (1997).

    MathSciNet  Google Scholar 

  16. K. S. Matviichuk, “Technical stability of the process of motion of two connected platforms carrying moving flywheels,”Izv. Ros. Akad. Nauk. Mekh. Tverd. Tela. No. 6, 3–10 (1993).

  17. K. S. Matviichuk, “Technical stability of parametrically excited distributed processes,”Prikl. Mat. Mekh.,50, Issue 2, 210–218 (1986).

    MathSciNet  Google Scholar 

  18. V. M. Matrosov, L. Yu. Anapol’skii, and S. N. Vasil’ev,Comparison Method in the Mathematical Theory of Systems [in Russian], Nauka, Novosibirsk (1980).

    Google Scholar 

  19. S. N. Vasil’ev, “Controllability of nonlinear systems under phase restrictions and constantly acting perturbations,”Izv. Ros. Akad. Nauk, Tekhn. Kibern., No. 1, 77–82 (1993).

  20. B. I. Babkin, “On the Chaplygin theorem on differential inequalities,”Mat. Sb.,46, No. 4, 389–398 (1958).

    MathSciNet  Google Scholar 

  21. J. Szarski,Differential Inequalities, PWN, Warszawa (1967).

    MATH  Google Scholar 

  22. B. Skalmierski and A. Tylikowski,Stabilnosc Ukladow Dynamicznych, PWN, Warszawa (1973).

    Google Scholar 

  23. M. A. Lavrent’ev and L. A. Lyusternik,Foundations of Variational Calculus [in Russian], Vol. 1, Part 1, ONTI, Moscow-Leningrad (1935).

    Google Scholar 

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Authors and Affiliations

  1. Institute of Mechanics, Ukrainian Academy of Sciences, Kiev

    K. S. Matviichuk

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  1. K. S. Matviichuk
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Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 12, pp. 1645–1658, December, 1999.

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Matviichuk, K.S. Technical stability of autonomous control systems with variable structure. Ukr Math J 51, 1858–1874 (1999). https://doi.org/10.1007/BF02525130

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  • DOI: https://doi.org/10.1007/BF02525130

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