Abstract
AbstractThis 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 nite interval is bounded and the er ge 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 signi cant improvement over previous one.
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