Cooperative Design of Asynchronous Controller and Dynamic Packet Dropouts Compensator for Strictly Dissipative T–S Fuzzy Markov Jump Systems

This article is dedicated to the problem of asynchronous state feedback control for Takagi–Sugeno (T–S) fuzzy Markov jump systems subject to randomly occurring network packet dropouts, in which the conditional probability matrix is partially known. A major novelty here is that an asynchronous fuzzy dynamic packet dropouts compensator is proposed based upon the information of the system dynamic for packet dropouts compensation in sensor-to-controller channel, which can obtain more accurate loss data estimation results. Meanwhile, in cooperation with the controller, the proposed compensator shares the same membership functions (MFs) and modes as the controller, providing a more reasonable structure and bringing less conservatism. To tackle the dual asynchronous phenomenon characterized by asynchronous modes and mismatched MFs simultaneously, an asynchronous nonparallel distributed compensation controller is presented with the idea of hidden Markov model. Furthermore, the asynchronous control strategy is investigated to guarantee the strictly dissipative and stochastically stable performance of the augmented closed-loop systems under the condition of partially known CPM. Less conservative criteria is guaranteed by introducing Lyapunov functionals with mode dependence and fuzzy basis dependence. Finally, two practical examples are presented to illustrate the validation of the proposed strategies.