Event-based Sliding Mode Control for Markovian Jump Systems with Time-varying Delays: An Observer Method

This paper is concerned with the observer-based sliding mode control (OBSMC) problem for Markovian jump systems with time-varying delays under the event-triggered protocol (ETP). Firstly, the ETP is introduced with hope to decrease the communication burden and determine whether the signal should be updated. Due to the fact that the system state is immeasurable, an observer is designed based on the measurement subsequently. Furthermore, by means of Lyapunov functional scheme, sufficient conditions ensuring the stochastic stability of sliding mode dynamics are obtained. Moreover, an event-triggered sliding mode control law is designed to drive the state trajectories onto a pre-defined sliding vicinity. Finally, the effectiveness of the proposed OBSMC method is verified with the aid of a simulation example.