Control of Discrete-Time State-Multiplicative Systems with Polytopic Region of Uncertainty

Design conditions for existence of linear state feed-back control for uncertain discrete-time stochastic systems with state-multiplicative noise, whose region of uncertainty is a polytope, are presented in the paper. Adapting the enhanced form of the bounded real lemma for this class of systems, an LMI based procedure is provided for computation of the gain matrix of linear state control law, giving conditions guaranteeing the resultant closed-loop systems to be asymptotically stable. The approach is illustrated by example demonstrating the validity of the proposed method.