Fault tolerant synchronization of chaotic systems based on T－S fuzzy model with fuzzy sampled-data controller

In this paper the fault tolerant synchronization of two chaotic systems based on fuzzy model and sample data is investigated. The problem of fault tolerant synchronization is formulated to study the global asymptotical stability of the error system with the fuzzy sampled-data controller which contains a state feedback controller and a fault compensator. The synchronization can be achieved no matter whether the fault occurs or not. To investigate the stability of the error system and facilitate the design of the fuzzy sampled-data controller, a Takagi--Sugeno (T--S) fuzzy model is employed to represent the chaotic system dynamics. To acquire the good performance and produce less conservative analysis result, a new parameter-dependent Lyapunov--Krasovksii functional and a relaxed stabilization technique are considered. The stability conditions based on linear matrix inequality are obtained to achieve the fault tolerant synchronization of the chaotic systems. Finally, a numerical simulation is shown to verify the results.