Stability analysis of delayed Markovian jump systems with delay switching and state signals and applications

Abstract

AbstractThis article addresses the asymptotical mean square stability problem of continuous‐time delayed Markovian jump systems (MJSs). Different from the existing delayed MJS models, time‐varying delays are contained in not only system state but also switching signal and could lead to great difficulties. An auxiliary system approach is developed to handle the difficulties, in which the traditionally delayed state and a new delayed exponential matrix are both involved. Based on the established model, sufficient stability conditions with solvable forms are given by using a Lyapunov function approach and some novel techniques. More extensions about an MJS under sampled switching and state signals are further considered, and so does the stabilization problem. A numerical example is offered to verify the effectiveness and superiority of the methods proposed in this study.