Robust chaos synchronization based on adaptive fuzzy delayed feedback H _∞ control

In this paper, we propose a new adaptive H _∞ synchronization strategy, called an adaptive fuzzy delayed feedback H _∞ synchronization (AFDFHS) strategy, for chaotic systems with uncertain parameters and external disturbances. Based on Lyapunov-Krasovskii theory, Takagi- Sugeno (T-S) fuzzy model and adaptive delayed feedback H _∞ control scheme, the AFDFHS controller is presented such that the synchronization error system is asymptotically stable with a guaranteed H8 performance. It is shown that the design of the AFDFHS controller with adaptive law can be achieved by solving a linear matrix inequality (LMI), which can be easily facilitated by using some standard numerical packages. An illustrative example is given to demonstrate the effectiveness of the proposed AFDFHS approach.