Skip to main content
SpringerLink
Log in

On the stability of a trivial invariant torus of one class of impulsive systems

  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

We consider the problem of asymptotic stability of the trivial invariant torus of one class of impulsive systems. Sufficient criteria of asymptotic stability are obtained by the method of freezing in one case, and by the direct Lyapunov method for the investigation of stability of solutions of impulsive systems in another case.

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, Differential Equations with Pulse Influence [in Russian], Vyshcha Shkola, Kiev (1987).

    Google Scholar 

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

    Google Scholar 

  3. B. F. Bylov, R. É. Vinograd, D. M. Grobman, and V. V. Nemytskii, Theory of Lyapunov Exponents and Its Applications to Problems of Stability [in Russian], Nauka, Moscow (1966).

    Google Scholar 

  4. B. P. Demidovich, Lectures on the Mathematical Theory of Stability [in Russian], Nauka, Moscow (1967).

    Google Scholar 

  5. Yu. A. Mitropol’skii, A. M. Samoilenko, and V. L. Kulik, Investigation of the Dichotomy of Linear Systems of Differential Equations with the Use of Lyapunov Functions [in Russian], Naukova Dumka, Kiev (1990).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Kiev University, Kiev

    S. I. Dudzyanyi & N. A. Perestyuk

Authors
  1. S. I. Dudzyanyi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. N. A. Perestyuk
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 3, pp. 338–349, March, 1998.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dudzyanyi, S.I., Perestyuk, N.A. On the stability of a trivial invariant torus of one class of impulsive systems. Ukr Math J 50, 387–399 (1998). https://doi.org/10.1007/BF02528804

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02528804

Keywords

Search

Navigation