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Zbl 1153.93030
Zhang, Weihai; Huang, Yulin; Xie, Lihua
Infinite horizon stochastic $H_2/H_\infty $control for discrete-time systems with state and disturbance dependent noise. (English)
[J] Automatica 44, No. 9, 2306-2316 (2008). ISSN 0005-1098

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 2000:: *93E03 General theory of stochastic systems
93C55 Discrete-time control systems
90C25 Convex programming

Keywords: discrete-time stochastic systems; state and disturbance-dependent noise; bounded realness; $H_{2}/H_\infty $ control; coupled matrix-valued equations

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Zentralblatt MATH Berlin [Germany]