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

Authors
  • Korenevskii, D. G.1
  • 1 Institute of Mathematics, Ukrainian Academy of Sciences, Kiev , Kiev
Type
Published Article
Journal
Mathematical Notes
Publisher
Kluwer Academic Publishers-Plenum Publishers
Publication Date
Jul 01, 2001
Volume
70
Issue
1-2
Pages
192–205
Identifiers
DOI: 10.1023/A:1010202824752
Source
Springer Nature
Keywords
License
Yellow

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).

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