Event‐triggered sliding mode control for stochastic Markov switching systems with Lévy noise and time‐varying delays

Abstract This paper investigates a sliding mode control strategy under the event‐triggered mechanism for a class of stochastic Markov switching systems subject to Lévy noise and time‐varying delays. Firstly, a sliding mode surface function is designed with an integral term. Then both the generalized Itô formula and the Gronwall inequality are used to verify the exponential stability of the system on this sliding mode surface in the mean‐square sense. Secondly, an event‐triggered sliding mode control strategy is designed to guarantee the sliding mode surface's reachability. Thirdly, the positive lower bound on the triggering interval is also given to exclude Zeno behavior. In the end, the validity of the theoretical derivation is confirmed through a numerical simulation.