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Infinite horizon stochastic H 2 /H 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 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.
93E03General theory of stochastic systems
93C55Discrete-time control systems
90C25Convex programming