Static output feedback H_∞ control for discrete-time Markov jump linear systems

This paper investigates the problem of static output feedback H _∞ control for discrete-time Markov jump systems (MJSs) with partly unknown transition probabilities. Two design methods are presented to deal with it respectively. First, similar to the existing method of dealing with the unknown part of transition probabilities and with the help of the Finsler's Lemma, two sets of slack variables with special structure are introduced to decouple the product terms of system matrices and Lyapunov matrices among different operation modes, and hence provide a mode-dependent static output feedback H_∞ controllers design method. Second, by making full use of the available information on the known part of the transition probabilities, a new method is presented with simple design conditions. The resulting designs guarantee that the closed-loop system is stochastically stable with prescribed H_∞ performance. A numerical example is given to illustrate the superiority and the effectiveness of the proposed controller design methods.