Observer-Based Sliding Mode Control for Markov Jump Systems with Actuator Failures and Asynchronous Modes

The brief studies the asynchronous observer-based sliding mode control (SMC) for Markov jump systems (MJSs) with actuator failures. Considering the phenomena of unmeasurable states and the case that the controller/observer to be devised have different modes from the original systems, a hidden Markov model (HMM) is used to construct an asynchronous observer and the corresponding sliding surface is designed. Then, the asynchronous SMC strategy is developed to guarantee the reachability of the predetermined sliding surface in a limited time. A sufficient condition is established for the mean-square stability of the overall closed-loop systems and the desired controller is designed. Moreover, when the conditional probabilities describing the mode asynchronism are only partially known for the HMM in the systems, the related results are also given. Finally, simulation results show the usefulness of the developed techniques.