Stability analysis of continuous-time Markovian jump time-delay systems with time-varying transition rates

This paper investigates the stability problem of Markovian jump systems. The systems under consideration include time-varying delay and time-varying transition rates. The time-varying transition rate matrix in continuous-time domain is considered to lie in a convex bounded domain. By constructing a parameter-dependent Lyapunov functional and fully considering the information about the rate of change of time-varying parameters, a parameter-dependent stochastic stability condition is derived. Furthermore, based on the structure characteristics of Lyapunov matrix and transition rate matrix, the parameter-dependent matrix inequality is converted into a finite set of linear matrix inequalities (LMIs). A numerical example is presented to demonstrate the effectiveness of the theoretical results.