Journal of Applied Mathematics
Volume 2013 (2013), Article ID 856282, 10 pages
Research Article

Adaptive Sliding Mode Controller Design for Projective Synchronization of Different Chaotic Systems with Uncertain Terms and External Bounded Disturbances

1Department of Industry Design, Tianjin University of Science and Technology, Tianjin 300457, China
2Department of Electrical and Mining Engineering, University of South Africa, Florida 1710, South Africa
3Department of Automation, Nankai University, Tianjin 300071, China

Received 22 January 2013; Accepted 1 June 2013

Academic Editor: Constantinos Siettos

Copyright © 2013 Shijian Cang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Synchronization is very useful in many science and engineering areas. In practical application, it is general that there are unknown parameters, uncertain terms, and bounded external disturbances in the response system. In this paper, an adaptive sliding mode controller is proposed to realize the projective synchronization of two different dynamical systems with fully unknown parameters, uncertain terms, and bounded external disturbances. Based on the Lyapunov stability theory, it is proven that the proposed control scheme can make two different systems (driving system and response system) be globally asymptotically synchronized. The adaptive global projective synchronization of the Lorenz system and the Lü system is taken as an illustrative example to show the effectiveness of this proposed control method.