Chaotic synchronization using backstepping method with application to the Chua's circuit and Lorenz system

In this paper, backstepping method is proposed for synchronizing chaotic systems. The tool consists in a recursive procedure that combines the choice of a Lyapunov function with the design of feedback control. It offers a systematic design procedure for the synchronization of a large class of continuous-time hyper-chaotic systems, which implies that much complicated high-order chaotic systems can be used to improve the security in chaos communications. In order to illustrate the general applicability of backstepping design. the tool is used to synchronize the dynamics of Chua's circuits and Lorenz systems. Numerical simulations are presented to show the effectiveness of this approach.