Stochastic stability analysis of nonlinear semi-Markov jump systems with time delays and incremental quadratic constraints

Abstract The article proposes a kind of stability analysis method for nonlinear time-delayed semi-Markov jump systems with incremental quadratic constraints. To meet the requirement of stochastic stability, the sufficient conditions formulated by linear matrix inequalities are derived. Both the transition rate of semi-Markov process and the time delay are time-varying, which make the considered system more general than the systems governed by Markov process and whose time delay is invariant. The mode-dependent Lyapunov-Krasovskii function is employed to analyze the stability problem. Besides, incremental quadratic constraints are proposed to reduce the conservatism of sufficient conditions. Finally, the effectiveness and superiority of the proposed method is verified by an example of virus mutation treatment model.