Almost Sure Stability of Markov Jump Systems With Persistent Dwell Time Switching

This article investigates the exponential almost sure stability (EAS-stability) of switching Markov jump systems (SMJSs). The considered SMJSs are ruled by Markov jump switching and deterministic switching simultaneously. The deterministic switching follows the persistent dwell time (PDT) switching which is more general than the dwell time (DT) switching and the average DT (ADT) switching. To tackle the difficulties caused by PDT switching, a new method is constructed by restricting the deterministic switching frequency into a suitable range. First, the detailed parameter analyzing is presented because the general measure parameter is unable to describe the dynamic characteristic of SMJSs with PDT switching. Second, the switching rule is established on account of the restricted switching frequency. Two sufficient conditions are further proposed to ensure the EAS-stability of SMJSs with all stable subsystems and SMJSs containing unstable subsystems, respectively. A numerical example and a fault-prone system model are given to illustrate the effectiveness of the proposed strategies.