A BRL for A Class of Discrete-time Markov Jump Linear System with Piecewise-Constant TPs

摘要

This paper aims to obtain a Bounded Real Lemma (BRL) for a class of Markov jump linear systems (MJLSs) with time-varying transition probabilities (TPs) in discrete-time domain. The time-varying character of TPs is considered as piecewise-constant and the variation of TP matrices is subject to average dwell time (ADT) switching, i.e., the number of switches in a finite interval is bounded and the average time between two consecutive switchings of TP matrices is not less than a constant. Combining the Lyapunov function approach and the linear matrix inequality technique, a BRL for the underlying system is derived in order to check whether the corresponding system is stochastically stable and has a guaranteed H_∞ noise-attenuation performance index scheduled based on the variation of TP matrices. A numerical example is provided to demonstrate that the method obtained in this paper is a significant improvement over previous one.