Stability Analysis for a Class of Discrete-Time Nonhomogeneous Markov Jump Systems with Multiplicative Noises

Abstract

This paper is concerned with a class of discrete-time nonhomogeneous Markov jump systems with multiplicative noises and time-varying transition probability matrices which are valued on a convex polytope. The stochastic stability and finite-time stability are considered. Some stability criteria including infinite matrix inequalities are obtained by parameter-dependent Lyapunov function. Furthermore, infinite matrix inequalities are converted into finite linear matrix inequalities (LMIs) via a set of slack matrices. Finally, two numerical examples are given to demonstrate the validity of the proposed theoretical methods.