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Infinite horizon stochastic $H_2/H_\infty$control for discrete-time systems with state and disturbance dependent noise. (English) Zbl 1153.93030
Summary: This paper studies the infinite horizon mixed $H_{2}/H_\infty$ 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 $H_{2}/H_\infty$ controller is equivalent to the solvability of four coupled matrix-valued equations. A suboptimal $H_{2}/H_\infty$ controller design is given based on a convex optimization approach and an iterative algorithm is proposed to solve the four coupled matrix-valued equations.

##### MSC:
 93E03 General theory of stochastic systems 93C55 Discrete-time control systems 90C25 Convex programming
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##### References:
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