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

Kang Xu

doi:doi:10.11648/j.ml.20180403.13

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

Kang Xu

Published in Mathematics Letters (Volume 4, Issue 3)

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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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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Author Information

Kang Xu

Anhui Huitong Space Geographic Information Technology Co., Ltd, Hefei, China

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Plain Text BibTeX RIS

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

Copy | Download

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

Copy | Download

@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}
}

Copy | Download

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  -

Copy | Download