Adaptive Synchronization of Uncertain Chaotic Systems Based on T–S Fuzzy Model

This paper presents an adaptive approach for synchronization of Takagi-Sugeno (T-S) fuzzy chaotic systems. T-S fuzzy model can represent a general class of nonlinear system and we employ it for fuzzy modeling of the chaotic drive system. Since the output of the drive system is only available for synchronization, the response system is designed based on fuzzy adaptive observer for uncertain parameters and parameter mismatch cases. We analyze the stability of the overall fuzzy synchronization system by applying Lyapunov stability theory and derive stability conditions by solving linear matrix inequalities (LMIs) problem. The adaptive law is derived to estimate the uncertain parameters or parameter mismatch. Numerical examples are given to demonstrate the validity of the proposed fuzzy adaptive synchronization approach.