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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:
93E03General theory of stochastic systems
93C55Discrete-time control systems
90C25Convex programming
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References:
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