Further Results on Stability Analysis of Discrete-Time Markov Jump Linear Systems with Time-Varying Delay and Partly Known Transition Probabilities

Xingang Zhao,Yiwen Zhao,Jianda Han

doi:10.1155/2015/524584

Abstract

This paper is concerned with the stability analysis of discrete-time Markov jump linear systems (MJLSs) with time-varying delay and partly known transition probabilities. The time delay is varying between lower and upper bounds, and the partly known transition probabilities cover the cases of known, uncertain with known lower and upper bounds, and completely unknown, which is more general than the existing result. Via constructing an appropriate Lyapunov function and employing a new technique to separate Lyapunov variables from unknown transition probabilities, a novel stability criterion is obtained in the framework of linear matrix inequality. A numerical example is given to show the effectiveness of the proposed approach.

Highlights

Markov jump linear systems (MJLSs), a class of stochastic systems, have been widely applied in manufacturing systems, power systems, aerospace systems, and networked control systems
This paper is concerned with the stability analysis of discrete-time Markov jump linear systems (MJLSs) with time-varying delay and partly known transition probabilities
Via constructing an appropriate Lyapunov function and employing a new technique to separate Lyapunov variables from unknown transition probabilities, a novel stability criterion is obtained in the framework of linear matrix inequality

Summary

Introduction

Markov jump linear systems (MJLSs), a class of stochastic systems, have been widely applied in manufacturing systems, power systems, aerospace systems, and networked control systems. To be consistent with the actual situation, transition probabilities in [28,29,30,31,32] are assumed to be known or unknown With this assumption, stability analysis of MJLSs with time-varying delay is investigated in [32]. Stability analysis of MJLSs with time-varying delay is investigated in [32] In these results, when transition probabilities are unknown with known lower and upper bounds, they are treated as completely unknown, which may cause conservativeness.

System Description and Preliminaries

Main Results

Illustrative Example

Conclusions