Stochastic H2/H∞ control for discrete-time systems with multiplicative noise in state and control input: Infinite horizon case

This paper studies the infinite horizon mixed H₂/H_infin control for linear discrete-time systems with stochastic multiplicative noise in state and control input. We shall first establish a version of stochastic bounded real lemma (SBRL). Based on the SBRL, we show that the existence of a static state feedback H₂/H_infin controller is equivalent to the solvability of four coupled matrix-valued equations. For some special case, a suboptimal H₂/H_infin controller design algorithm is also given based on convex optimization.