H ∞ mean square finite-time control for Markov jump linear system with multiple equilibria

Abstract

In this article, the mean square finite-time $H_{\infty }$ control problems of two types of Markov jump linear system with multiple equilibria are investigated. To be specific, Markov jump linear system with multiple equilibria in discrete-time domain and continuous-time domain are considered, respectively, in which the equilibria of subsystems are different. First, an average equilibrium is introduced to equivalently reformulate the initial system expressions. Following this method, some sufficient conditions guaranteeing that Markov jump linear system with multiple equilibria subjected to norm bounded disturbance is mean square finite-time boundedness are proposed, and the results are extended to $H_{\infty }$ mean square finite-time boundedness. Then, mean square finite-time $H_{\infty }$ controllers are designed separately to stabilize the two types of Markov jump linear system with multiple equilibria and also achieve the prescribed $H_{\infty }$ performance index. The proposed methods in this article are a natural generalization of typical results in Markov jump linear system sharing common equilibrium. Finally, two numerical examples are exploited to demonstrate the effectiveness of the methods proposed in this article.