Synchronization of Harb - Zohdy chaotic system via backstepping design

Abstract

In this article, the backstepping method is used to synchronize Harb-Zohdi chaotic system. Firstly, the control for the synchronization of chaotic systems Harb-Zohdi is considered with no unknown parameters. Next, an adaptive backstepping control law is derived to generate an error signal between the drive system Harb-Zohdi and response system Harb-Zohdi with an uncertain parameter asymptotically synchronized. Finally, this method is extended to synchronize the system with two unknown parameters. In this paper, the stability analysis is proved by using Lyapunov stability theorem. Note that the method presented here needs only one controller to realize the synchronization. Numerical simulations indicate the effectiveness of the proposed chaos synchronization scheme.