Criteria of the mean-square asymptotic stability of solutions of systems of linear stochastic difference equations with continuous time and delay

被引：0

作者：

Korenevskii D.G. ^{[1
]}

机构：

[1] Institute of Mathematics, Ukrainian Academy of Sciences, Kiev

来源：

Ukrainian Mathematical Journal | 1998年 / 50卷 / 8期

关键词：

Difference Equation; Lyapunov Function; Asymptotic Stability; Linear Difference Equation; Sylvester Equation;

D O I：

10.1007/BF02513094

中图分类号：

学科分类号：

摘要：

We obtain spectral and algebraic coefficient criteria and sufficient conditions for the mean-square asymptotic stability of solutions of systems of linear stochastic difference equations with continuous time and delay. We consider the case of a rational correlation between delays and a "white-noise"-type stochastic perturbation of coefficients. We use the method of Lyapunov functions. Most results are presented in terms of the Sylvester and Lyapunov matrix algebraic equations. © 1999 Kluwer Academic/Plenum Publishers.

引用

页码：1224 / 1232

页数：8

共 5 条

[1] Korenevskii D.G., On the asymptotic stability of solutions of systems of deterministic and stochastic linear stationary difference equations with delay, Dokl. Akad Nauk SSSR, 322, 2, pp. 219-223, (1992)
[2] Korenevskii D.G., Kaizer K., Coefficient conditions for the asymptotic stability of solutions of systems of linear difference equations with continuous time and delay, Ukr. Mat. Zh., 50, 4, pp. 516-522, (1998)
[3] Zhabko A.P., Kharitonov V.L., Methods of Linear Algebra in Problems of Control, (1993)
[4] Korenevskii D.G., Stability of Dynamical Systems under Random Perturbations of Parameters. Algebraic Criteria, (1989)
[5] Korenevskii D.G., Algebraic coefficient criterion of the convergence 'with reserve' (exponential stability) for solutions of linear stationary difference equations, Dokl. Akad Nauk SSSR, 313, 6, pp. 1320-1323, (1990)

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