A Switched Vertices Approach to Stability Analysis of Delayed Markov Jump Systems With Time-Varying Transition Rates

In the last five years, the stability of continuous-time Markov jump systems (MJSs) with time-varying transition rates (TRs) has been widely investigated by establishing parameter-dependent Lyapunov-Krasovskii functional (PDLKF), in which the time-varying TRs are considered to be in a polytopic sense. However, in the previous works, the derivative of polytopic parameters in PDLKF is assumed to be in a finite domain, which is limited in actual applications. In this brief, a switched vertices approach is proposed to remove the bounded assumption. On this basis, a new stability criterion is derived to guarantee the MJSs to be stochastically stable, which is more general and practical than the existing results. An example is illustrated to show the effectiveness of the obtained result.