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

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Abstract

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 Lü system, and fractional-order Duffing system.

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Acknowledgements

The present work is supported by National Natural Science Foundation of China (No. 11202155). And the authors would like to thank the editor and the reviewers for their constructive comments and suggestions.

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  1. Department of Mathematics, Xidian University, Xi’an, 710071, P.R. China

    Ruihong Li & Weisheng Chen

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  1. Ruihong Li
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  2. Weisheng Chen
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Correspondence to Ruihong Li.

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Li, R., Chen, W. Lyapunov-based fractional-order controller design to synchronize a class of fractional-order chaotic systems. Nonlinear Dyn 76, 785–795 (2014). https://doi.org/10.1007/s11071-013-1169-0

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