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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.

93C55Discrete-time control systems
93D09Robust stability of control systems
93C40Adaptive control systems
93C73Perturbations in control systems
93E15Stochastic stability
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