Stochastic \(H^\infty\). (English) Zbl 0914.93019

The paper considers stochastic linear plants which are controlled by dynamic output feedback and subject to both deterministic and stochastic perturbations. The objective is to develop an \(H^{\infty}\)-type theory for such systems. Necessary and sufficient conditions for the existence of a stabilizing compensator are obtained. These conditions keep the effect of the perturbations on the to-be-controlled output below a given threshold \(\gamma >0.\) The connection between \(H^{\infty}\) theory and stability radii is discussed and leads to a lower bound for the radii, which is shown to be tight in some special cases.


93B36 \(H^\infty\)-control
93C55 Discrete-time control/observation systems
93D09 Robust stability
93C40 Adaptive control/observation systems
93C73 Perturbations in control/observation systems
93E15 Stochastic stability in control theory
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