Stochastic stability analysis of Markovian jump systems with additive mode-dependent time-varying delays and partially known transition rates

Abstract

This paper focuses on the stochastic stability of the Markovian jump systems with two additive mode-dependent time-varying delays and partially known transition rates. First, a novel mode-dependent Lyapunov-Krasovskii functional (LKF) is constructed and the single integral terms in the derivative of LKF are estimated by the generalised free-weighting-matrix-based integral inequality. Then, some stability criteria in terms of linear matrix inequalities are obtained by using the convex combination technique. Finally, two numerical examples are presented to illustrate the feasibility of the proposed method.