An adaptive H _∞ exponential lag synchronization scheme for uncertain disturbed chaotic systems

In this paper, the problem of adaptive H _∞ exponential lag synchronization (AHELS) for chaotic systems with unknown parameters and external disturbances is studied. Based on Lyapunov theory and linear matrix inequality (LMI) formulation, the AHELS controller is designed and an analytic expression of the controller with its adaptive laws of parameters is shown. The proposed AHELS controller can guarantee adaptive exponential lag synchronization of both drive and response systems with unknown parameters. Furthermore, this controller reduces the effect of external disturbances to an H _∞ norm constraint. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed method.