Stability and stabilisation of Itô stochastic systems with piecewise homogeneous Markov jumps

Abstract

ABSTRACTThis paper focuses on the problem of stability and stabilisation for continuous-time Itô stochastic Markovian jump linear systems with time-varying transition rates. The time-varying property of the transition rates is considered to be finite piecewise homogeneous. Firstly, the stability conditions of the piecewise homogeneous Itô stochastic Markovian jump linear systems are given in terms of linear matrix inequalities (LMIs). Especially, a novel stability criterion is developed for the considered systems by the existence of the unique positive-definite solution of the corresponding coupled Lyapunov matrix equations. Secondly, two state-feedback controllers are designed via LMIs to stabilise the systems. Finally, a practical example is provided to illustrate the effectiveness of the presented theoretical results.