Fault-Tolerant Synchronization of Chaotic Systems with Fuzzy Sampled Data Controller Based on Adaptive Event-Triggered Scheme

This paper deals with the problem of the fault-tolerant fuzzy master–slave systems synchronization through an adaptive event-triggered scheme (AETS). First, a Takagi–Sugeno (T–S) fuzzy model is employed to represent the master–slave system dynamics. Second, an AETS is introduced to judge whether the newly sampled controller’s signals should be released to the slave system or not. Consequently, the less computation resources and network bandwidth are utilized under the AETS. Meanwhile, a novel adaptive law is designed to achieve the threshold of event-triggering condition on-line. Third, a novel fuzzy controller is designed, containing a state feedback controller and a fault compensator to achieve the fault-tolerant synchronization, which is formulated to study the global asymptotical stability of the error system. As a results, applying Lyapunov theory and inequality technique, new sufficient condition is obtained to guarantee the stability of the error system. Further, the controller gain and the weight of event-triggering condition are designed through linear matrix inequalities (LMIs) approach. Finally, a numerical simulation example is employed to demonstrate the practical utility of this method.