H∞-type control for discrete-time stochastic systems

In this paper we consider discrete-time, linear stochastic systems with random state and input matrices which are subjected to stochastic disturbances and controlled by dynamic output feedback. The aim is to develop an H-infinity-type theory for such systems. For this class of systems a stochastic bounded real lemma is derived which provides the basis for a linear matrix inequality (LMI) approach similar to, but more general than the one presented in Reference 1. for stochastic differential systems. Necessary and sufficient conditions are derived for the existence of a stabilizing controller which reduces the norm of the closed-loop perturbation operator to a level below a given threshold gamma. These conditions take the form of coupled nonlinear matrix inequalities. In the absence of the stochastic terms they get reduced to the linear matrix inequalities of deterministic H-infinity-theory for discrete time systems. Copyright (C) 1999 John Wiley & Sons, Ltd.