Stability control of fractional chaotic systems based on a simple Lyapunov function

Volume 10, Issue 9, pp 4876--4889 http://dx.doi.org/10.22436/jnsa.010.09.28

Publication Date: September 22, 2017 Submission Date: April 13, 2017

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Authors

Tianzeng Li - School of Mathematics and Statistics, Artificial Intelligence Key Laboratory of Sichuan Province, Sichuan university of Science and Engineering, Zigong 643000, China. Yu Wang - School of Mathematics and Statistics, Key Laboratory of Higher Education of Sichuan Province for Enterprise Informationalization and Internet of Things, Sichuan university of Science and Engineering, Zigong 643000, China. Hongmei Li - School of Economic and Management, Northwest University, Xi'an 710069, China.

Abstract

In this paper the stabilization of fractional-order chaotic systems and a new property of fractional derivatives are studied. Then we propose a new fractional-order extension of Lyapunov direct method and a control method based on a simple Lyapunov candidate function. The proposed control method can be applied to the stabilization of fractional-order chaotic and hyperchaotic systems. This control method is simple, universal, and theoretically rigorous. Numerical simulations are given for three fractional-order chaotic (or hyperchaotic) systems to verify the effectiveness and the universality of the proposed control method.

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Keywords

• Lyapunov function
• fractional-order
• stabilization

MSC

•  93D05
•  93D15

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