Infinite Horizon H_2/H_∞ Control for Discrete-Time Time-Varying Markov Jump Systems with Multiplicative Noise

摘要

In this paper we consider the infinite horizon H_2/H_∞ control problem for discrete-time time-varying 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 state- and disturbance-multiplicative noises. Based on which, a necessary and sufficient condition is provided for the existence of linear state feedback H_2/H_∞ controller in terms of four coupled discrete-time Riccati difference equations. Finally, a concluding remark and some open topics are proposed.