Infinite horizon H2/H∞ control for discrete-time time-varying Markov jump systems with multiplicative noise

In this paper we consider the infinite horizon H2/H∞ control problem for discrete-time timevarying linear systems subject to Markov jump parameters and state-multiplicative noises. A stochastic bounded real lemma is firstly developed for a class of discrete-time time-varying Markov jump systems with stateand disturbance-multiplicative noises. Based on which, a necessary and sufficient condition is provided for the existence of linear state feedback H2/H∞ controller in terms of four coupled discretetime Riccati difference equations. Finally, a concluding remark and some open topics are proposed.