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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 948782, 7 pages
Research Article

Synchronization of Fractional-Order Chaotic Systems with Gaussian Fluctuation by Sliding Mode Control

Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an 710072, China

Received 4 September 2013; Accepted 23 October 2013

Academic Editor: Jinhu Lü

Copyright © 2013 Yong Xu and Hua Wang. 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.


Chaotic systems are always influenced by some uncertainties and external disturbances. This paper investigates the problem of practical synchronization of fractional-order chaotic systems with Gaussian fluctuation. A fractional integral (FI) sliding surface is proposed for synchronizing the uncertain fractional-order system, and then the sliding mode control technique is carried out to realize the synchronization of the given systems. One theorem about sliding mode controller is presented to prove that the proposed controller can make the system achieve synchronization. As a case study, the presented method is applied to the fractional-order Chen-Lü system, and simulation results show that the proposed control approach is capable to go against Gaussian noise well.