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

TL;DR

This paper investigates finite-time stability and stabilization of linear discrete time-varying stochastic systems with multiplicative noise, providing necessary and sufficient conditions and practical LMI-based methods for analysis and control.

Contribution

It introduces new criteria for finite-time stability and stabilization using state transition matrices and Lyapunov functions with LMIs, applicable to time-varying stochastic systems.

Findings

Derived necessary and sufficient conditions for finite-time stability.

Developed LMI-based methods for stabilization analysis.

Validated results with numerical examples.

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.