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

Abstract

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 tau(t) is assumed to satisfy tau 1 <= tau(t) <= tau(2). Based on the flexible terminal approach, the timevarying delay t(t) is first transformed such that tau(1)(t) <= tau(t) <= tau 2 (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. (c) 2018 Elsevier Inc. All rights reserved.