Stabilization of discrete-time Markovian jump systems with partially unknown transition probabilities

Abstract

In this paper the stabilization problem for a class of discrete-time Markovian jump system with partially unknown transition probabilities is investigated via using the time-delayed and impulsive controllers. As some elements in transition matrix are unknown, a new approach is proposed to estimate the unknown elements, in which an impulsive stabilizing controller depending on time delays and system mode is presented in terms of linear matrix inequalities (LMIs) with equality constraints. Especially, if there are no time delays and impulsive effects in the controller, it is derived that the conditions for the existence of H∞ controller can be expressed by LMIs without equality constraints. Finally, illustrative examples are presented to show the benefits and the validity of the proposed approaches.