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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 Stochastic systems in control theory (general)
93C55 Discrete-time control/observation systems
90C25 Convex programming
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