Chaos Suppression of a Class of Fractional-Order Chaotic Systems with Order Lying in (1, 2)
Mathematics Letters
Volume 4, Issue 3, September 2018, Pages: 51-58
Received: Sep. 25, 2018; Accepted: Oct. 30, 2018; Published: Dec. 4, 2018
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Author
Kang Xu, Anhui Huitong Space Geographic Information Technology Co., Ltd, Hefei, China
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Abstract
It is shown that fractional-order (FO) nonlinear systems can also show higher nonlinearity and complex dynamics. FO chaotic systems have wider applications in secure communication, signal processing, financial field due to FO chaos has larger key space and more complex random sequences than integer-order chaos. Thanks to the lack of the effective analytical methods and controller design methods of integer-order chaotic systems can not be applied directly to FO chaos systems, to control chaos of FO chaotic systems is a very interesting and difficult problem, especially for FO chaotic system with order α:1<α<2. Based on the stability theory of FO systems and the linear state feedback control, an LMI criterion for controlling a class of fractional-order chaotic systems with fractional-order α:1<α<2 is addressed in this paper. The proposed method can be easily verified and resolved by using the Matlab LMI toolbox. Moreover, the proposed controller is linear, easy to implement and overcome some defects in the recent literature, which have improved the existing results. The method employed in this letter can effectively avoid control cost and inaccuracy in the literatures, and can be be applied to FO hyperchaos systems and synchronization controller design of FO chaotic system. Theoretical analysis and numerical simulations are presented to demonstrate the validity and feasibility of the proposed methods.
Keywords
Fractional-Order Chaotic Systems, Linear Control, Linear Matrix Inequality
To cite this article
Kang Xu, Chaos Suppression of a Class of Fractional-Order Chaotic Systems with Order Lying in (1, 2), Mathematics Letters. Vol. 4, No. 3, 2018, pp. 51-58. doi: 10.11648/j.ml.20180403.13
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Copyright © 2018 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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