## $$H^\infty$$-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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### References:

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