A flexible terminal approach to stochastic stability and stabilization of continuous-time semi-Markovian jump systems with time-varying delay.

This paper addresses the stochastic stability and stabilization problems for a class of semi-Markovian jump systems (SMJSs) with time-varying delay, where the time-varying delay τ(t) is assumed to satisfy τ1 ≤ τ(t) ≤ τ2. Based on the flexible terminal approach, the time-varying delay τ(t) is first transformed such that τ1(t) ≤ τ(t) ≤ τ2(t). By utilizing a novel semi-Markovian Lyapunov Krasoviskii functional (SMLKF) and an improved reciprocally convex inequality (RCI), sufficient conditions are established to guarantee a feasible solution. Two illustrated examples are shown the effectiveness of the main results.