H∞ Control for a Class of Discrete-Time Infinite State Markov Jump Systems

The control problem of a class of discrete-time stochastic systems affected by multiplicative noise and infinite Markov jump parameters is studied. Firstly, a linear inequality about the solution of Riccati equation is given, and a controller is constructed by solving the linear inequality. Secondly, the bounded real lemma in infinite time domain of discrete-time stochastic systems is given by using the knowledge of operator theory and stochastic analysis. Through a coupled Riccati equation, the equivalence between the solution of linear inequality and bounded real lemma is proved.