Skip to main content
SpringerLink
Log in

A method of stabilization of dynamic systems under constant perturbations

  • Published:
Cybernetics and Systems Analysis Aims and scope

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. A. M. Lyapunov, General Problem on Stability of Motion [in Russian], Fizmatgiz, Moscow (1959).

    Google Scholar 

  2. G. V. Shchipanov, “Theory and methods of controller design,” Avtomat. Telemekh, No. 1, 49–66 (1939).

  3. G. Zames, “Feedback and optimal sensitivity: model reference transformations, multiplicative seminorms, and approximate inverses,” IEEE Trans. Automat. Contr., AC-26, 301-320 (1981).

    Google Scholar 

  4. V. S. Kulebyakin, Theory of Invariance of Automatically Regulated and Controlled Systems, Proceedings of the First International Congress IFAC , The theory of Continuous Systems. Special Mathematical Problems, Izd. AN SSSR (1961).

  5. N. N. Luzin and P. I. Kuznetsov, “Absolute invariance and invariance toε in the theory of differential equations,” Dokl. Akad. Nauk SSSR,51, No. 4, 247–249 (1946).

    Google Scholar 

  6. B. N. Petrov, The invariance principle and condition of its application to calculation of linear and nonlinear systems, Proceedings of the First International Congress IFAC, The theory of Continuous Systems. Special Mathematical Problems, Izd. AN SSSR (1961).

  7. A. A. Stoorvogel, The H∞ Control Problem: a State Space Approach, Prentice Hall, Englewood Cliffs (1992).

    MATH  Google Scholar 

  8. T. Basar and P. Bernhard, H∞-Optimal Control and Related Minimax Design Problems, Birkhauser (1990).

  9. R. Kaiman, The General Theory of Control Systems, Proceedings of the First International Congress IFAC, Izd. AN SSSR (1961).

  10. A. M. Letov, “Analytical construction of controllers,” Avtomat. Telemekh, No. 4, 436-4141 (1960), No. 5, 561-569, No. 6, 661-665.

  11. H. Kwakernaak and R. Sivan, Linear Optimal Control Systems [Russian translation], Mir, Moscow (1977).

    Google Scholar 

  12. K. T. Leondes (ed.), Filtering and Stochastic Control in Dynamic Systems [Russian translation], Mir, Moscow (1980).

    Google Scholar 

  13. R. Isaacs, Differential Games [Russian translation], Mir, Moscow (1967).

    MATH  Google Scholar 

  14. N. N. Krasovskii and A. I. Subbotin, Position Differential Games [in Russian], Nauka, Moscow (1976).

    Google Scholar 

  15. R. F. Gabasov, F. M. Kirillova, and E. A. Kostina, “Closed state feedback for optimization of uncertain control systems. I. Single closure,” Avtomat. Telemekh., No. 7, 121-130 (1996).

  16. R. F. Gabasov, F. M. Kirillova, and O. I. Kostyukova, “Methods of stabilization of dynamic systems,” Izv. RAN, Tekhn. Kibernetika, No. 3, 67–77 (1994).

    Google Scholar 

  17. N. V. Balashevich, R. Gabasov, and F. M. Kirillova, “Program-Position Optimization of Dynamic Systems,” Kibern. Sist. Anal., No. 1, 66–73 (1994).

  18. R. F. Gabasov and F. M. Kirillova, “Real-time construction of optimal closable feedbacks,” Proc 13th World Congr. IFAC (San Francisco, June 30–July 5, 1996, Vol. D.

  19. R. F. Gabasov, F.M. Kirillova, and S.V. Prischepova, Optimal feedback control, Lect. Notes Control and Inform. Sci., Springer-Verlag, London, 207, (1995).

    Google Scholar 

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

    Google Scholar 

  21. P. V. Bromberg, Matrix Methods in the Theory of a Relay Impulse Controller [in Russian], Nauka, Moscow (1967).

    Google Scholar 

  22. R. F. Gabasov, F. M. Kirillova, and A. I. Tyatyushkin, Constructive Optimization Methods. Part 1. Linear Problems [in Russian], Universitetskoye, Minsk (1984).

    MATH  Google Scholar 

  23. G. Dantzig, Linear Programming and Extensions [Russian translation], Progress, Moscow (1966).

    MATH  Google Scholar 

Download references

Authors
  1. R. F. Gabasov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. E. A. Ruzhitskaya
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This work has been carried out with financial support from the Fundamental Research Fund of the Republic of Belarus (grant F97M-139).

Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 120–130, March–April, 1999.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gabasov, R.F., Ruzhitskaya, E.A. A method of stabilization of dynamic systems under constant perturbations. Cybern Syst Anal 35, 279–289 (1999). https://doi.org/10.1007/BF02733475

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02733475

Keywords

Search

Navigation