Observer-based Event-triggered Sliding Mode Control for Markov Jump Systems with Partially Unknown Transition Probabilities

This paper investigates the event-triggered sliding mode control problem for discrete-time Markov jump systems under the unavailable states and partially unknown transition probabilities. To save the limited computational source, an event-triggered scheme is implemented to determine whether the current data should be sent or not, and an observer is constructed to estimate the unmeasurable states of the system. Then, on the basis of the Lyapunov functional technique, the sufficient conditions of stochastic stability for the closed-loop system are derived. Moreover, the sliding mode controller based on event-triggered mechanism is designed to ensure that the state trajectories of the closed-loop system can be driven onto the predefined sliding manifold and maintain there for all subsequent time. Finally, a numerical example is utilized to demonstrate the effectiveness of the proposed method.