Skip to main content
SpringerLink
Log in

On Stability of Integral Sets of Impulsive Differential Systems

  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

We introduce the notion of stability of integral sets of impulsive differential systems of general form (with nonfixed times of impulse influence). We establish conditions sufficient for the stability of an integral set.

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. G. K. Kulev and D. D. Bainov, “Global stability of sets for impulsive differential systems by Lyapunov's direct method,” Comput. Math. Appl., 19, No. 2, 17–28 (1990).

    Google Scholar 

  4. D. D. Bainov and I. M. Stamova, “Stability of sets for impulsive differential-difference equations with variable impulsive perturbations,” Commun. Appl. Nonlin. Anal., 5, No. 1, 69–81 (1998).

    Google Scholar 

  5. T. Yoshizawa, “Stability of sets and perturbed systems,” Funkc. Ekvacioj, 5, 31–69 (1962).

    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., Issue 23, 33–40 (1981).

  8. S. I. Gurgula, “Investigation of stability of solutions of impulsive systems by the second Lyapunov method,” Ukr. Mat. Zh., 34, No. 1, 100–103 (1982).

    Google Scholar 

  9. A. M. Samoilenko, “Investigation of dynamical systems by using functions of constant sign,” Ukr. Mat. Zh., 24, No. 3, 374–384 (1972).

    Google Scholar 

  10. V. I. Zubov, Stability of Motion [in Russian], Vysshaya Shkola, Moscow (1973).

    Google Scholar 

  11. N. G. Bulgakov, “On stability of invariant sets,” Differents. Uravn., 18, No. 2, 187–194 (1982).

    Google Scholar 

  12. A. O. Ignat'ev, “Application of the direct Lyapunov method to the investigation of integral sets,” Ukr. Mat. Zh., 44, No. 10, 1342–1348 (1992).

    Google Scholar 

  13. V. Lakshmikantham, S. Leela, and A. A. Martynyuk, Stability of Motion: Comparison Method [in Russian], Naukova Dumka, Kiev (1991).

    Google Scholar 

  14. X. Z. Liu, “Stability results for impulsive differential systems with applications to population-growth models,” Dynamics Stability Syst., 9, No. 2, 163–174 (1994).

    Google Scholar 

  15. M. U. Akhmetov and N. A. Perestyuk, “Comparison method for impulsive differential equations,” Differents. Uravn., 26, No. 9, 1475–1483 (1990).

    Google Scholar 

  16. M. O. Perestyuk and O. S. Chernikova, “On stability of invariant sets of discontinuous dynamical systems,” Ukr. Mat. Zh., 53, No. 1, 78–84 (2001).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Shevchenko Kiev University, Kiev

    M. O. Perestyuk & O. S. Chernikova

Authors
  1. M. O. 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, M.O., Chernikova, O.S. On Stability of Integral Sets of Impulsive Differential Systems. Ukrainian Mathematical Journal 54, 306–315 (2002). https://doi.org/10.1023/A:1020146815128

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1020146815128

Keywords

Search

Navigation