Stochastic stability and stabilization conditions of semi-Markovian jump systems with mode transition-dependent sojourn-time distributions

This paper is concerned with the stochastic stability and stabilization problem for a class of continuous-time semi-Markovian jump systems (S-MJSs) with mode transition-dependent sojourn-time distributions. In contrast to other approaches, this paper offers the possibility to explore more refined probability models on the sojourn-time by considering the mode transition-dependent sojourn-time distributions instead of mode-dependent ones. Here, to construct a finite set of linear matrix inequalities (LMIs) from sojourn-time-dependent matrix inequalities, a less conservative relaxation method is proposed in such a way that all available constraints on time-varying transition rates can be exploited. Simulation examples report the effectiveness of the proposed method.