Asynchronous observer-based sliding mode control for 2-D Markov jump Roesser systems

This article deals with the state reconstruction and sliding mode control problem for continuous-time two-dimensional Roesser systems. Aiming at the phenomena of mode mismatch between the controlled system and the controller, the asynchronous control strategy is employed by constructing the conditional probability matrix and utilizing the hidden Markov model. Considering not full state information is unavailable in some practical applications, the observer-based sliding mode control scheme is developed. Two types of sliding mode surfaces are synthesized based on system state and observer state, respectively. Accordingly, different sliding mode control laws are synthesized for these two scenarios to ensure the resulting system trajectories to reach onto the prescribed sliding mode surfaces. Sufficient conditions are provided to guarantee the stochastic stability for corresponding overall closed-loop systems. Finally, the feasibility and effectiveness of the proposed method are verified by numerical simulations.