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Chaos Suppression of a Class of Fractional-Order Chaotic Systems with Order Lying in (1, 2)

Received: 25 September 2018     Accepted: 30 October 2018     Published: 4 December 2018
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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.

Published in Mathematics Letters (Volume 4, Issue 3)
DOI 10.11648/j.ml.20180403.13
Page(s) 51-58
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2018. Published by Science Publishing Group

Keywords

Fractional-Order Chaotic Systems, Linear Control, Linear Matrix Inequality

References
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Cite This Article
  • APA Style

    Kang Xu. (2018). Chaos Suppression of a Class of Fractional-Order Chaotic Systems with Order Lying in (1, 2). Mathematics Letters, 4(3), 51-58. https://doi.org/10.11648/j.ml.20180403.13

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    ACS Style

    Kang Xu. Chaos Suppression of a Class of Fractional-Order Chaotic Systems with Order Lying in (1, 2). Math. Lett. 2018, 4(3), 51-58. doi: 10.11648/j.ml.20180403.13

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    AMA Style

    Kang Xu. Chaos Suppression of a Class of Fractional-Order Chaotic Systems with Order Lying in (1, 2). Math Lett. 2018;4(3):51-58. doi: 10.11648/j.ml.20180403.13

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  • @article{10.11648/j.ml.20180403.13,
      author = {Kang Xu},
      title = {Chaos Suppression of a Class of Fractional-Order Chaotic Systems with Order Lying in (1, 2)},
      journal = {Mathematics Letters},
      volume = {4},
      number = {3},
      pages = {51-58},
      doi = {10.11648/j.ml.20180403.13},
      url = {https://doi.org/10.11648/j.ml.20180403.13},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ml.20180403.13},
      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.},
     year = {2018}
    }
    

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  • TY  - JOUR
    T1  - Chaos Suppression of a Class of Fractional-Order Chaotic Systems with Order Lying in (1, 2)
    AU  - Kang Xu
    Y1  - 2018/12/04
    PY  - 2018
    N1  - https://doi.org/10.11648/j.ml.20180403.13
    DO  - 10.11648/j.ml.20180403.13
    T2  - Mathematics Letters
    JF  - Mathematics Letters
    JO  - Mathematics Letters
    SP  - 51
    EP  - 58
    PB  - Science Publishing Group
    SN  - 2575-5056
    UR  - https://doi.org/10.11648/j.ml.20180403.13
    AB  - 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.
    VL  - 4
    IS  - 3
    ER  - 

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