Asynchronous sliding mode control for Markov jump systems based on a dynamic event-triggered mechanism

This paper investigates the dynamic event-triggered asynchronous sliding mode control problem for Markovian jump systems. Considering the asynchronous phenomenon between the system modes and the controller modes, a novel dynamic event-triggered asynchronous integral-type sliding mode function is designed. With the help of advanced inequality techniques, a Lyapunov-Krasovskii function is constructed to guarantee the stability of the sliding mode dynamics. A dynamic event-triggered asynchronous sliding mode controller is designed such that the system trajectories can be driven onto the sliding mode surface in finite time and remain there thereafter. In addition, the dynamic event-triggered mechanism is developed to reduce network resources consumption, and the Zeno behavior is proven to be nonexistent. Finally, two examples are provided to demonstrate the effectiveness of the theoretical results.