INVARIANT DENSITY, LYAPUNOV EXPONENT, AND ALMOST SURE STABILITY OF MARKOVIAN-REGIME-SWITCHING LINEAR SYSTEMS

作     者：Qi HE Gang George YIN 

作者机构：Department of Mathematics Wayne State University Detroit MI 48202 USA 

出 版 物：《Journal of Systems Science & Complexity》 (系统科学与复杂性学报（英文版）)

年 卷 期：2011年第24卷第1期

页      面：79-92页

核心收录：

学科分类：0711[理学-系统科学] 07[理学] 08[工学] 070201[理学-理论物理] 081101[工学-控制理论与控制工程] 0811[工学-控制科学与工程] 071102[理学-系统分析与集成] 081103[工学-系统工程] 0702[理学-物理学] 

基　　金：This research was supported in part by the National Science Foundation under Grant No. DMS-0907753  in part by the Air Force Office of Scientific Research under Grant No. FA9550-10-1-0210  and in part by the National Natural Science Foundation of China under Grant No. 70871055 

主　　题：Invariant density Lyapunov exponent randomly switching ordinary differential equation. 

摘      要：This paper is concerned with stability of a class of randomly switched systems of ordinary differential equations. The system under consideration can be viewed as a two-component process （X（t）, α（t））, where the system is linear in X（t） and α（t） is a continuous-time Markov chain with a finite state space. Conditions for almost surely exponential stability and instability are obtained. The conditions are based on the Lyapunov exponent, which in turn, depends on the associate invaxiant density. Concentrating on the case that the continuous component is two dimensional, using transformation techniques, differential equations satisfied by the invariant density associated with the Lyapunov exponent are derived. Conditions for existence and uniqueness of solutions are derived. Then numerical solutions are developed to solve the associated differential equations.