Skip to main content
SpringerLink
Log in

Stability of difference rational systems

  • Brief Communications
  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

For systems of difference equations with rational functions on the right-hand sides represented in a unified vector matrix form, we obtain stability conditions and calculate a value of the radius of a disk for the domain of asymptotic stability on the basis of the second Lyapunov method.

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. N. Sharkovskii, Yu. L. Maistrenko, and E. Yu. Romanenko,Difference Equations and Their Applications [in Russian], Naukova Dumka, Kiev (1986).

    Google Scholar 

  2. Ya. Z. Tsypkin and Yu. S. Popkov,Theory of Nonlinear Pulse Systems [in Russian], Nauka, Moscow (1973).

    Google Scholar 

  3. R. Bellman and K. L. Cooke,Differential-Difference Equations, Academic Press New York (1963).

    MATH  Google Scholar 

  4. P. V. Bromberg,Matrix Methods in the Theory of Relay and Pulse Control [in Russian], Nauka, Moscow (1967).

    Google Scholar 

  5. K. G. Valeev and G. S. Finin,Construction of Lyapunov Functions [in Russian], Naukova Dumka, Kiev (1981).

    MATH  Google Scholar 

  6. D. I. Martynyuk,Lectures on Qualitative Theory of Difference Equations [in Russian], Naukova Dumka, Kiev (1972).

    Google Scholar 

  7. E. A. Barbashin,Lyapunov Functions [in Russian], Nauka, Moscow (1970).

    Google Scholar 

  8. A. Halanay and D. Wexler,Qualitative Theory of Pulse Systems [Russian translation], Mir, Moscow (1971)

    Google Scholar 

  9. S. Zhang, “Razumikhin techniques in delay difference systems,”Pan American Math. J.,3, No. 2, 1–16 (1933).

    Google Scholar 

  10. D. Ya. Khusainov and E. E. Shevelenko, “Study of the stability of differential systems with rational right-hand sides,”Ukr. Mat. Zh.,47, No. 9, 1295–1299 (1995).

    Article  MATH  MathSciNet  Google Scholar 

Download references

Authors
  1. D. Ya. Khusainov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. E. E. Shevelenko
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Kiev University, Kiev. Translated from Ukrainskii Matermaticheskii Zhurnal, Vol. 51, No. 3, pp. 428–431, March, 1999.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Khusainov, D.Y., Shevelenko, E.E. Stability of difference rational systems. Ukr Math J 51, 476–479 (1999). https://doi.org/10.1007/BF02592486

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02592486

Keywords

Search

Navigation