Skip to main content
SpringerLink
Log in

On the Stability of Invariant Sets of Discontinuous Dynamical Systems

  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

We establish sufficient conditions for the stability, asymptotic stability, and instability of invariant sets of discontinuous dynamical systems.

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. A. M. Samoilenko and N. A. Perestyuk, Impulsive Differential Equations [in Russian], Vyshcha Shkola, Kiev (1987).

    Google Scholar 

  2. A. M. Samoilenko and N. A. Perestyuk, Impulsive Differential Equations World Scientific, Singapore (1995).

    Google Scholar 

  3. A. M. Samoilenko, Elements of the Mathematical Theory of Multifrequency Vibrations [in Russian], Nauka, Moscow (1987).

    Google Scholar 

  4. A. M. Samoilenko, “Investigation of dynamical systems with the use of functions of constant sign,” Ukr. Mat. Zh. 24, No. 3, 374–384 (1972).

    Google Scholar 

  5. V. F. Rozhko, “On the theory of discontinuous systems. I. Invariant and dynamical limit sets. Poisson Stability,” Mat. Issled. 4, Issue 3, 63–73 (1969).

    Google Scholar 

  6. S. I. Gurgula and N. A. Perestyuk, “On the second Lyapunov method in impulsive systems,” Dokl. Akad. Nauk Ukr. SSR, Ser. A No. 10, 11–14 (1982).

  7. S. I. Gurgula and N. A. Perestyuk, “On stability of solutions of impulsive systems,” Vestn. Kiev Univ., Mat. Mekh. No. 23, 33–40 (1981).

  8. N. A. Perestyuk and O. S. Chernikova, “Stability of solutions of impulsive systems,” Ukr. Mat. Zh. 49, No. 1, 98–111 (1997).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Kiev University, Kiev

    N. A. Perestyuk & O. S. Chernikova

Authors
  1. N. A. Perestyuk
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. O. S. Chernikova
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Perestyuk, N.A., Chernikova, O.S. On the Stability of Invariant Sets of Discontinuous Dynamical Systems. Ukrainian Mathematical Journal 53, 91–98 (2001). https://doi.org/10.1023/A:1010492901900

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1010492901900

Keywords

Search

Navigation