Asynchronous Sliding Mode Control of Networked Markov Jump Systems via an Asynchronous Observer Approach Based on a Dynamic Event Trigger

This paper explores the utilization of sliding mode control, which relies on an asynchronous observer, for Markov jump systems subject to external disturbances. Firstly, given that the system’s mode is not directly measurable and could potentially differ from the observer’s and controller’s mode, the paper constructs an asynchronous observer employing a hidden Markov model. Secondly, a sliding surface is designed to correspond with the asynchronous observer. Moreover, a multi-parameter event-triggered mechanism is incorporated into the observer design to alleviate bandwidth strain. Thirdly, by applying the integrated sliding mode control law, we ensure that the system state trajectories will reach the sliding surface within a finite time. Fourthly, the achievement of H∞ stability is realized by making use of the Lyapunov function. Lastly, a practical-oriented example is presented to illustrate the efficiency of the established method.