Skip to main content
SpringerLink
Log in

Robust dissipativity of discrete systems and its investigation with the help of a sequence of sets of Lyapunov functions

  • Published:
Cybernetics and Systems Analysis Aims and scope

Abstract

A generalized concept of robust dissipativity is introduced and theorems on the analysis of this property are formulated and proved with the help of the Lyapunov functions method. It is proposed to use a specially constructed sequence of sets of Lyapunov functions that can allow one to improve the initial estimate of the boundary set of a dissipative system up to the establishment of the asymptotic robust stability property in the limiting case. An example of investigating the dissipativity of a linear discrete system with unknown parameters under additive perturbation is given.

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

Similar content being viewed by others

References

  1. P. V. Bromberg, Stability and Self-Oscillations of Pulse Control Systems [in Russian], Oborongiz, Moscow (1953).

    Google Scholar 

  2. R. E. Kalman and J. E. Bertram, “Control systems analysis and design via the Second Method of Liapunov. II. Discrete-time systems,” ASME Trans., Ser. D, Journ. of Basic Engineer., 82, No. 2 (1960).

  3. V. M. Kuntsevich and Yu. N. Chekhovoi, Nonlinear Control Systems with Pulse-and Pulse-Width Modulation [in Russian], Tekhnika, Kiev (1970).

    Google Scholar 

  4. R. A. Nelepin (ed.), Methods of Investigation of Nonlinear Automatic Control Systems [in Russian], Nauka, Moscow (1975).

    Google Scholar 

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

    Google Scholar 

  6. Ya. I. Zyelyk and M. M. Lychak, “Computer technology of interval-set analysis in MATLAB,” Cybernetics and Systems Analysis, No. 1, 122–139 (2004).

  7. V. M. Kuntsevich and M. M. Lychak, “Elements of the theory of set evolution and stability of these processes,” Cybernetics, No. 1, 105–111 (1983).

  8. V. M. Kuntsevich and M. M. Lychak, Synthesis of Optimal and Adaptive Control Systems: The Game Approach [in Russian], Naukova Dumka, Kiev (1985).

    MATH  Google Scholar 

  9. M. M. Lychak, “A new approach to the investigation of stability of nonlinear dynamic systems,” Avtomatika, No. 1, 38–45 (1980).

  10. M. M. Lychak, “Stability criteria based on dissipativity estimates,” Probl. Upravlen. Inf., No. 5, 61–68 (1997).

Download references

Author information

Authors and Affiliations

  1. Institute of Space Research, National Academy of Sciences and National Space Agency of Ukraine, Kiev, Ukraine

    M. M. Lychak

Authors
  1. M. M. Lychak
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. M. Lychak.

Additional information

__________

Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 13–23, March–April 2008.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lychak, M.M. Robust dissipativity of discrete systems and its investigation with the help of a sequence of sets of Lyapunov functions. Cybern Syst Anal 44, 161–169 (2008). https://doi.org/10.1007/s10559-008-0016-7

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10559-008-0016-7

Keywords

Search

Navigation