Stochastic admissibility of singular Markov jump systems with time-delay via sliding mode approach

•Constructed integral type sliding mode switching functions for each Markov jump subsystem.•Linear matrix inequalities and sufficient conditions for stochastic admissibility are given.•The sliding mode controller and switching rules are designed by Lyapunov stability method.•The state trajectory can reach the sliding mode surface in a limited time, resulting in stable sliding mode dynamics. In this article, stochastic admissibility of singular Markov jumping systems (SMJSs) with time-varying delays is studied by sliding mo de control (SMC) method. Firstly, we construct integral-type sliding mode switching functions for each Markov jump subsystem, next, we construct some linear matrix inequalities(LMI) and sufficient conditions for stochastic admissibility are given. Then the sliding mo de controller and switching rules are designed by Lyapunov stability method, the state trajectory can reach the sliding mode surface (SMS) in a limited time, resulting in stable sliding mode dynamics. Finally, two examples are given to illustrate the effectiveness and feasibility of the proposed scheme.