Infinite horizon stochastic control for discrete-time systems with state and disturbance dependent noise

This paper studies the infinite horizon mixed H 2 / H ∞ control for discrete-time stochastic systems with state and disturbance dependent noise. We shall first establish a version of stochastic bounded real lemma (SBRL) which by itself has theoretical importance. Based on the SBRL, it is shown that under the condition of exact observability, the existence of a static state feedback H 2 / H ∞ controller is equivalent to the solvability of four coupled matrix-valued equations. A suboptimal H 2 / H ∞ controller design is given based on a convex optimization approach and an iterative algorithm is proposed to solve the four coupled matrix-valued equations.