H-infinity-type control for discrete-time stochastic systems

In this paper we consider discrete-time, linear stochastic systems with ran dom state and input matrices which are subjected to stochastic disturbances and controlled by dynamic output feedback. The aim is to develop an H-infi nity-type theory for such systems. For this class of systems a stochastic b ounded real lemma is derived which provides the basis for a linear matrix i nequality (LMI) approach similar to, but more general than the one presente d in Reference 1. for stochastic differential systems. Necessary and suffic ient conditions are derived for the existence of a stabilizing controller w hich reduces the norm of the closed-loop perturbation operator to a level b elow a given threshold gamma. These conditions take the form of coupled non linear matrix inequalities. In the absence of the stochastic terms they get reduced to the linear matrix inequalities of deterministic H-infinity-theo ry for discrete time systems. Copyright (C) 1999 John Wiley & Sons, Ltd.