Lyapunov-based fractional-order controller design to synchronize a class of fractional-order chaotic systems

作者：Li, Ruihong^*; Chen, Weisheng

来源：Nonlinear Dynamics, 2014, 76(1): 785-795.

DOI：10.1007/s11071-013-1169-0

• Fractional-order chaotic system
• Adaptive fractional-order feedback
• Commensurate and incommensurate system
• Barbalat lemma

In this paper, a novel adaptive fractional-order feedback controller is first developed by extending an adaptive integer-order feedback controller. Then a simple but practical method to synchronize almost all familiar fractional-order chaotic systems has been put forward. Through rigorous theoretical proof by means of the Lyapunov stability theorem and Barbalat lemma, sufficient conditions are derived to guarantee chaos synchronization. A wide range of fractional-order chaotic systems, including the commensurate system and incommensurate case, autonomous system, and nonautonomous case, is just the novelty of this technique. The feasibility and validity of presented scheme have been illustrated by numerical simulations of the fractional-order Chen system, fractional-order hyperchaotic Lu system, and fractional-order Duffing system.

• 出版日期2014-4
• 单位西安电子科技大学