Mean-square strong stability and stabilization of discrete-time stochastic systems with multiplicative noises

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.

Automated summary

This article investigates the mean-square strong stability and stabilization of a discrete-time stochastic system corrupted by multiplicative noises. Necessary and sufficient conditions for the mean-square (MS) strong stability are derived, and the relationship between MS-strong stability and MS-stability is given. Moreover, conditions and controller designs for achieving mean-square strong stabilization via state feedback and output feedback are presented.