Ukrainian Mathematical Journal

, Volume 54, Issue 8, pp 1355–1366 | Cite as

Stochastic Lyapunov Functions for a System of Nonlinear Difference Equations

  • I. A. Dzhalladova


We study problems related to the stability of solutions of nonlinear difference equations with random perturbations of semi-Markov type. We construct Lyapunov functions for different classes of nonlinear difference equations with semi-Markov right-hand side and establish conditions for their existence.


Difference Equation Lyapunov Function Random Perturbation Nonlinear Difference Equation Construct Lyapunov Function 
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  1. 1.
    I. I. Gikhman and A. V. Skorokhod, Stochastic Differential Equations and Their Applications [in Russian], Naukova Dumka, Kiev (1982).Google Scholar
  2. 2.
    V. S. Korolyuk and A. V. Svishchuk, Semi-Markov Random Evolutions [in Russian], Naukova Dumka, Kiev (1992).Google Scholar
  3. 3.
    R. Z. Khas'minskii, Stability of Systems of Differential Equations under Random Perturbations [in Russian], Nauka, Moscow (1969).Google Scholar
  4. 4.
    V. S. Pugachev and I. N. Sinitsyn, Stochastic Differential Systems [in Russian], Nauka, Moscow (1990).Google Scholar
  5. 5.
    K. G. Valeev and I. A. Dzhalladova, “Optimization of nonlinear systems of stochastic difference equations,” Ukr. Mat. Zh., 54, No. 1, 3–15 (2002).Google Scholar
  6. 6.
    I. Ya. Kats and N. N. Krasovskii, “On stability of systems with random parameters,” Prikl. Mat. Mekh., No.5, 809–823 (1960).Google Scholar
  7. 7.
    K. G. Valeev, N. N. Karelova, and V. I. Gorelov, Optimization of Linear Systems with Random Coefficients [in Russian], Izd. Ross. Univ. Druzhby Narodov, Moscow (1996).Google Scholar

Copyright information

© Plenum Publishing Corporation 2002

Authors and Affiliations

  • I. A. Dzhalladova
    • 1
  1. 1.Kiev National Economic UniversityKiev

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