Stability and stabilization of continuous-time stochastic Markovian jump systems with random switching signals

This paper investigates the stability and stabilization problems of continuous-time stochastic Markovian jump systems (SMJSs) with random switching signals, in which diffusions are included. Here, the dwell time of each subsystem consists of fixed and random parts. The stability condition for such general SMJSs is firstly presented. Then, new sufficient condition for stabilizing mode-dependent controllers is provided in terms of LMIs and could be solved directly. The proposed results show that all the features of the underlying systems such as diffusion and random switching signal play important roles in the system analysis and synthesis of exponentially mean-square stability. Because of the obtained results with LMI forms, they may be extended to more general cases that the transition rate matrix (TRM) is uncertain or partially unknown. Finally, numerical examples are used to demonstrate the effectiveness of the proposed methods.