Lyapunov theorems for stability and semistability of discrete-time stochastic systems

被引：15

作者：

Haddad, Wassim M. ^{[1
]}

Lee, Junsoo ^{[1
]}

机构：

[1] Georgia Inst Technol, Sch Aerosp Engn, Atlanta, GA 30332 USA

来源：

AUTOMATICA | 2022年 / 142卷

关键词：

Stochastic stability and semistability; Discrete-time systems; Lyapunov and converse Lyapunov theorems; CONVERGENCE; ATTRACTORS; CONTINUUM; TESTS;

D O I：

10.1016/j.automatica.2022.110393

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

This paper develops Lyapunov and converse Lyapunov theorems for discrete-time stochastic semistable nonlinear dynamical systems expressed by Ito-type difference equations possessing a continuum of equilibria. Specifically, we provide necessary and sufficient Lyapunov conditions for stochastic semistability and show that stochastic semistability implies the existence of a continuous Lyapunov function whose difference operator involves a discrete-time analog of the infinitesimal generator for continuous-time Ito dynamical systems and decreases along the dynamical system sample solution sequences satisfying an inequality involving the average distance to the set of the system equilibria. (C) 2022 Elsevier Ltd. All rights reserved.

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页数：9

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