This article investigates the mean-square strong stability and stabilization of a discrete-time stochastic system corrupted by multiplicative noises. First, the definition of the mean-square (MS) strong stability is addressed to avoid overshoots in system dynamics, and two necessary and sufficient conditions for the MS-strong stability are derived. Moreover, the relationship between MS-strong stability and MS-stability is given. Second, some necessary and sufficient conditions of the MS-strong stabilization via state feedback (SF) and output feedback are obtained, respectively. Furthermore, analytical expressions of SF controller and static output feedback (SOF) controller are proposed, respectively. Finally, an equivalent design method for SOF controller and dynamic output feedback controller is presented.

In this paper, the mean-square strong stability and stabilization of discrete-time Markov jump systems are studied. Firstly, the definition of mean-square strong stability is given, and the necessary and sufficient conditions for mean-square strong stability are derived. Secondly, several necessary and sufficient conditions for mean-square strong stabilization via a state feedback controller and an output feedback controller are obtained. Furthermore, explicit expressions for the state feedback controller and static output feedback controller are obtained. Finally, two examples are given to illustrate the validity of the above results.