Robust synchronization of perturbed Chen’s fractional-order chaotic systems

In this paper, based on a stability theorem proved for linear fractional-order systems, a scheme for robust synchronization of two perturbed fractional-order Chen systems is proposed. In the proposed scheme, both master and slave systems are considered to be involved with external disturbances having unknown values. It is analytically shown that any set of bounded external disturbances can be damped by the proposed method, where synchronization error will be forced and then kept inside a ball around the origin. Since during the design procedure the radius of this ball could be easily chosen by the designer, the synchronization can be done with any desired accuracy. The proposed method can be easily extended to synchronize other fractional-order chaotic systems. Numerical simulation results are presented to show the effectiveness of the proposed method.