Discrete-Time H∞ Control for Infinite Markov Jump Systems with Uncertainty

This paper discusses the H∞ control problem for uncertain discrete-time infinite Markov jump systems. Firstly, some sufficient conditions for existence of state feedback H∞ controller are given to ensure that the closed-loop system is exponentially mean square stable with conditioning (EMSS-C) for the zero exogenous disturbance with H∞ performance level. Further, the backward iterative algorithm of four coupled matrix Riccati equations (CMREs) is presented to design H2/ H∞ controller. Finally, some numerical simulations are provided to show the applicability of developed approaches.