Finite-time stability and stabilization of linear discrete time-varying stochastic systems

Abstract

This paper studies the finite-time stability and stabilization of linear discrete time-varying stochastic systems with multiplicative noise. Firstly, necessary and sufficient conditions for finite-time stability are presented via state transition matrix approach. Secondly, this paper also develops the Lyapunov function method to study finite-time stability and stabilization of discrete time-varying stochastic systems based on matrix inequalities and linear matrix inequalities (LMIs), so as to Matlab LMI Toolbox can be used. Two numerical examples are given to illustrate the effectiveness of the proposed results.