H∞ filteing for discrete-time Markov jump linear systems

Abstract

This paper investigates the problem of H∞ filtering for discrete-time Markov jump systems with partly unknown transition probabilities (TPs). The filter to be designed is assumed to be mode-dependent. Firstly, with the help of the Finsler's Lemma, two sets of slack variables with special structure are introduced to provide an improved mode-dependent H∞ filters design method with extra degrees of freedom. Then, with making use of the relationship of the known part of the TPs and the unknown part of the TPs sufficiently, a new simple design method is presented with less conservativeness. The resulting designs guarantee that the error system is stochastically stable with prescribed H∞ performance. A numerical example is given to illustrate the superiority and the effectiveness of the proposed filtering method.