Adaptive synchronization for uncertain chaotic systems with external disturbance

In this paper, we propose a new adaptive H ∞ synchronization scheme for chaotic systems with unknown parameter and external disturbance. Based on Lyapunov stability theory and linear matrix inequality (LMI) approach, the adaptive H ∞ synchronization controller is presented to not only guarantee stable synchronization but also reduce the effect of external disturbance to an H ∞ norm constraint. The proposed controller with adaptive law can be obtained by solving the LMI problem. The adaptive H ∞ synchronization problems for Chua’s chaotic system and hyperchaotic Rössler system are presented to show the effectiveness of the proposed chaos synchronization scheme.