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

Hinrichsen, D.; Pritchard, A. J.

SIAM J. Control Optimization 36, No. 5, 1504-1538 (1998).

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.

Reviewer: Vjatscheslav Vasiliev (Tomsk)

MSC:

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

Keywords:

stochastic systems; state dependent noise; \(H^{\infty}\) control; matrix inequalities; stabilization; dynamic output feedback; stability radii