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Matematicheskie Zametki, 2001, Volume 70, Issue 2, Pages 213–229
DOI: https://doi.org/10.4213/mzm735
(Mi mzm735)
 

This article is cited in 17 scientific papers (total in 17 papers)

Stability Criteria for Solutions of Systems of Linear Deterministic or Stochastic Delay Difference Equations with Continuous Time

D. G. Korenevskij

Institute of Mathematics, Ukrainian National Academy of Sciences
References:
Abstract: We give spectral and algebraic coefficient criteria (necessary and sufficient conditions) as well as sufficient algebraic coefficient conditions for the Lyapunov asymptotic stability of solutions to systems of linear deterministic or stochastic delay difference equations with continuous time under white noise coefficient perturbations for the case in which all delay ratios are rational. For stochastic systems, mean-square asymptotic stability is studied. The Lyapunov function method is used. Our criteria on algebraic coefficients and our sufficient conditions are stated in terms of matrix Lyapunov equations (for deterministic systems) and matrix Sylvester equations (for stochastic systems).
Received: 22.02.2001
English version:
Mathematical Notes, 2001, Volume 70, Issue 2, Pages 192–205
DOI: https://doi.org/10.1023/A:1010202824752
Bibliographic databases:
UDC: 517.929+519.248
Language: Russian
Citation: D. G. Korenevskij, “Stability Criteria for Solutions of Systems of Linear Deterministic or Stochastic Delay Difference Equations with Continuous Time”, Mat. Zametki, 70:2 (2001), 213–229; Math. Notes, 70:2 (2001), 192–205
Citation in format AMSBIB
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\by D.~G.~Korenevskij
\paper Stability Criteria for Solutions of Systems of Linear Deterministic or Stochastic Delay Difference Equations with Continuous Time
\jour Mat. Zametki
\yr 2001
\vol 70
\issue 2
\pages 213--229
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\zmath{https://zbmath.org/?q=an:1022.39003}
\transl
\jour Math. Notes
\yr 2001
\vol 70
\issue 2
\pages 192--205
\crossref{https://doi.org/10.1023/A:1010202824752}
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  • https://www.mathnet.ru/eng/mzm735
  • https://doi.org/10.4213/mzm735
  • https://www.mathnet.ru/eng/mzm/v70/i2/p213
  • This publication is cited in the following 17 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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