Adaptive Ξ∞ Synchronization of Unified Chaotic Systems

In this paper, the problem of adaptive Ξ_∞ synchronization for unified chaotic systems with unknown parameter and external disturbance is studied. It is noticed that this unified chaotic system contains the noted Lorentz, Lü and Chen systems. Based on Lyapunov theory and linear matrix inequality (LMI) formulation, the novel feedback controller with adaptive law is established to not only guarantee stable synchronization of both master and slave systems but also reduce the effect of external disturbance to an Ξ_∞ norm constraint. A criterion for existence of the controller is given in terms of LMIs. Finally, a numerical example shows the effectiveness of the proposed method.