New Approach to Feedback Stabilization of Linear Discrete Time-Varying Stochastic Systems
Tianliang Zhang, Shengyuan Xu, Weihai Zhang
Abstract
This article investigates uniform finite-time stabilization, mean square uniform stabilization, and mean square uniform asymptotic/exponential stabilization of linear discrete time-varying stochastic (LDTVS) systems. A new state transition matrix (STM) method is first used to study the feedback stabilization problem of LDTVS systems. Based on the STM method, necessary and sufficient conditions for the above concerned feedback stabilization issues are, respectively, presented in terms of STMs and generalized constrained Lyapunov equations/inequalities. More importantly, linear matrix inequality-based necessary and sufficient conditions are provided for uniform finite-time stabilization and mean square uniform stabilization, which are very convenient in the controller design. A practical example is proposed to show the effectiveness of our main results.