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\(H^\infty\)-type control for discrete-time stochastic systems. (English) Zbl 0934.93022

An \(H^{\infty}\)-type theory is developed for linear stochastic systems with random state and input matrices which are subjected to stochastic disturbances and controlled by dynamic output feedback. A bounded real lemma is derived to apply a linear matrix inequality approach to the problem. Conditions for existence of a stabilizing controller reducing the norm of the perturbation operator to a level below a given threshold are derived. This generalizes the known results in the non-stochastic case.

MSC:

93B36 \(H^\infty\)-control
93C55 Discrete-time control/observation systems
15A39 Linear inequalities of matrices
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