Asynchronous Control for Discrete‐Time Singular Markov Jump Systems With Incomplete Transition Probabilities and Actuator Saturation

ABSTRACT

This paper discusses the asynchronous control problem for discrete‐time singular Markov jump systems (SMJSs) with incomplete transition probabilities (TPs) and actuator saturation. A hidden Markov model (HMM) is employed to characterize the asynchronization behavior between the system and the controller, and the TPs of the system and the controller are not completely known. A convex hull approach is constructed to deal with the saturated non‐linearity. Firstly, some sufficient conditions to ensure the system is stochastically admissible (SA) with desired performance are obtained. Secondly, a novel approach is given to design the special structural controllers. Thirdly, the domain of attraction of the system is estimated. Finally, the effectiveness of the proposed approach is illustrated by simulations.