H 1 Type Control for Discrete - Time Stochasticsystemsa

In this paper we consider discrete-time, linear stochastic systems with random state and input matrices which are subject to stochastic disturbances and controlled by dynamic output feedback. The aim is to develop an H 1-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 14] for stochastic diierential systems. Necessary and suucient 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. These conditions take the form of coupled nonlinear matrix inequalities. In the absence of the stochastic terms they reduce to the linear matrix inequalities of deterministic H 1-theory for discrete time systems.