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Ukrainian Mathematical Journal

, Volume 52, Issue 12, pp 1942–1948 | Cite as

Criteria for the Asymptotic Stability of Solutions of Dynamical Systems

  • K. G. Valeev
  • I. A. Dzhalladova
Article
  • 18 Downloads

Abstract

We present a new proof for criteria for the asymptotic stability of systems of difference and differential equations based on the properties of monotone operators in a semiordered space. We also establish necessary and sufficient conditions for the asymptotic stability of stochastic systems of differential and difference equations in the mean square.

Keywords

Differential Equation Dynamical System Difference Equation Asymptotic Stability Stochastic System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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REFERENCES

  1. 1.
    K. G. Valeev and G. S. Finin, Construction of Lyapunov Functions[in Russian], Naukova Dumka, Kiev (1981).Google Scholar
  2. 2.
    A. M. Lyapunov, A General Problem on Stability of Motion[in Russian], Gostekhizdat, Moscow (1950).Google Scholar
  3. 3.
    D. G. Korenevskii, Stability of Dynamical Systems under Random Perturbations of Parameters[in Russian], Naukova Dumka, Kiev (1989).Google Scholar
  4. 4.
    D. G. Korenevskii, Stability of Solutions of Deterministic and Stochastic Differential-Difference Systems of Equations[in Russian], Naukova Dumka, Kiev (1992).Google Scholar

Copyright information

© Plenum Publishing Corporation 2000

Authors and Affiliations

  • K. G. Valeev
    • 1
  • I. A. Dzhalladova
    • 1
  1. 1.Kiev National Economical UniversityKiev

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