Adaptive Impulsive Synchronization for a Class of Delay Fractional-Order Chaotic System

Changyou Wang; Yuan Zhuo; Xingcheng Pu; Yonghong Li; Rui Li

doi:doi:10.11648/j.ajesa.20180602.11

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Adaptive Impulsive Synchronization for a Class of Delay Fractional-Order Chaotic System

Changyou Wang, Yuan Zhuo, Xingcheng Pu, Yonghong Li, Rui Li

Published in American Journal of Embedded Systems and Applications (Volume 6, Issue 2)

Received: 13 October 2018 Accepted: 31 October 2018 Published: 14 December 2018

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Abstract

This paper is concerned with the adaptive impulsive synchronization for a class of delay fractional-order chaotic system. Firstly, according to the impulsive differential equations theory and the adaptive control theory, the adaptive impulsive controller and the parametric update law are designed, respectively. Secondly, by constructing the suitable response system, the original fractional-order error system can be converted into the integral-order one. Finally, based on the Lyapunov stability theory and the generalized Barbalat’s lemma, some new sufficient conditions are derived to guarantee the asymptotic stability of synchronization error system.

Published in	American Journal of Embedded Systems and Applications (Volume 6, Issue 2)
DOI	10.11648/j.ajesa.20180602.11
Page(s)	69-74
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

Delay, Fractional-Order, Chaotic System, Impulsive, Synchronization

References

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APA Style

Changyou Wang, Yuan Zhuo, Xingcheng Pu, Yonghong Li, Rui Li. (2018). Adaptive Impulsive Synchronization for a Class of Delay Fractional-Order Chaotic System. American Journal of Embedded Systems and Applications, 6(2), 69-74. https://doi.org/10.11648/j.ajesa.20180602.11

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ACS Style

Changyou Wang; Yuan Zhuo; Xingcheng Pu; Yonghong Li; Rui Li. Adaptive Impulsive Synchronization for a Class of Delay Fractional-Order Chaotic System. Am. J. Embed. Syst. Appl. 2018, 6(2), 69-74. doi: 10.11648/j.ajesa.20180602.11

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AMA Style

Changyou Wang, Yuan Zhuo, Xingcheng Pu, Yonghong Li, Rui Li. Adaptive Impulsive Synchronization for a Class of Delay Fractional-Order Chaotic System. Am J Embed Syst Appl. 2018;6(2):69-74. doi: 10.11648/j.ajesa.20180602.11

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@article{10.11648/j.ajesa.20180602.11,
  author = {Changyou Wang and Yuan Zhuo and Xingcheng Pu and Yonghong Li and Rui Li},
  title = {Adaptive Impulsive Synchronization for a Class of Delay Fractional-Order Chaotic System},
  journal = {American Journal of Embedded Systems and Applications},
  volume = {6},
  number = {2},
  pages = {69-74},
  doi = {10.11648/j.ajesa.20180602.11},
  url = {https://doi.org/10.11648/j.ajesa.20180602.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajesa.20180602.11},
  abstract = {This paper is concerned with the adaptive impulsive synchronization for a class of delay fractional-order chaotic system. Firstly, according to the impulsive differential equations theory and the adaptive control theory, the adaptive impulsive controller and the parametric update law are designed, respectively. Secondly, by constructing the suitable response system, the original fractional-order error system can be converted into the integral-order one. Finally, based on the Lyapunov stability theory and the generalized Barbalat’s lemma, some new sufficient conditions are derived to guarantee the asymptotic stability of synchronization error system.},
 year = {2018}
}

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TY  - JOUR
T1  - Adaptive Impulsive Synchronization for a Class of Delay Fractional-Order Chaotic System
AU  - Changyou Wang
AU  - Yuan Zhuo
AU  - Xingcheng Pu
AU  - Yonghong Li
AU  - Rui Li
Y1  - 2018/12/14
PY  - 2018
N1  - https://doi.org/10.11648/j.ajesa.20180602.11
DO  - 10.11648/j.ajesa.20180602.11
T2  - American Journal of Embedded Systems and Applications
JF  - American Journal of Embedded Systems and Applications
JO  - American Journal of Embedded Systems and Applications
SP  - 69
EP  - 74
PB  - Science Publishing Group
SN  - 2376-6085
UR  - https://doi.org/10.11648/j.ajesa.20180602.11
AB  - This paper is concerned with the adaptive impulsive synchronization for a class of delay fractional-order chaotic system. Firstly, according to the impulsive differential equations theory and the adaptive control theory, the adaptive impulsive controller and the parametric update law are designed, respectively. Secondly, by constructing the suitable response system, the original fractional-order error system can be converted into the integral-order one. Finally, based on the Lyapunov stability theory and the generalized Barbalat’s lemma, some new sufficient conditions are derived to guarantee the asymptotic stability of synchronization error system.
VL  - 6
IS  - 2
ER  -

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Author Information

Changyou Wang

College of Automation, Chongqing University of Posts and Telecommunications, Chongqing, P. R. China
Yuan Zhuo

College of Automation, Chongqing University of Posts and Telecommunications, Chongqing, P. R. China
Xingcheng Pu

College of Automation, Chongqing University of Posts and Telecommunications, Chongqing, P. R. China
Yonghong Li

College of Science, Chongqing University of Posts and Telecommunications, Chongqing, P. R. China
Rui Li

College of Automation, Chongqing University of Posts and Telecommunications, Chongqing, P. R. China

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Plain Text BibTeX RIS

APA Style

Changyou Wang, Yuan Zhuo, Xingcheng Pu, Yonghong Li, Rui Li. (2018). Adaptive Impulsive Synchronization for a Class of Delay Fractional-Order Chaotic System. American Journal of Embedded Systems and Applications, 6(2), 69-74. https://doi.org/10.11648/j.ajesa.20180602.11

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ACS Style

Changyou Wang; Yuan Zhuo; Xingcheng Pu; Yonghong Li; Rui Li. Adaptive Impulsive Synchronization for a Class of Delay Fractional-Order Chaotic System. Am. J. Embed. Syst. Appl. 2018, 6(2), 69-74. doi: 10.11648/j.ajesa.20180602.11

Copy | Download

AMA Style

Changyou Wang, Yuan Zhuo, Xingcheng Pu, Yonghong Li, Rui Li. Adaptive Impulsive Synchronization for a Class of Delay Fractional-Order Chaotic System. Am J Embed Syst Appl. 2018;6(2):69-74. doi: 10.11648/j.ajesa.20180602.11

Copy | Download

@article{10.11648/j.ajesa.20180602.11,
  author = {Changyou Wang and Yuan Zhuo and Xingcheng Pu and Yonghong Li and Rui Li},
  title = {Adaptive Impulsive Synchronization for a Class of Delay Fractional-Order Chaotic System},
  journal = {American Journal of Embedded Systems and Applications},
  volume = {6},
  number = {2},
  pages = {69-74},
  doi = {10.11648/j.ajesa.20180602.11},
  url = {https://doi.org/10.11648/j.ajesa.20180602.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajesa.20180602.11},
  abstract = {This paper is concerned with the adaptive impulsive synchronization for a class of delay fractional-order chaotic system. Firstly, according to the impulsive differential equations theory and the adaptive control theory, the adaptive impulsive controller and the parametric update law are designed, respectively. Secondly, by constructing the suitable response system, the original fractional-order error system can be converted into the integral-order one. Finally, based on the Lyapunov stability theory and the generalized Barbalat’s lemma, some new sufficient conditions are derived to guarantee the asymptotic stability of synchronization error system.},
 year = {2018}
}

Copy | Download

TY  - JOUR
T1  - Adaptive Impulsive Synchronization for a Class of Delay Fractional-Order Chaotic System
AU  - Changyou Wang
AU  - Yuan Zhuo
AU  - Xingcheng Pu
AU  - Yonghong Li
AU  - Rui Li
Y1  - 2018/12/14
PY  - 2018
N1  - https://doi.org/10.11648/j.ajesa.20180602.11
DO  - 10.11648/j.ajesa.20180602.11
T2  - American Journal of Embedded Systems and Applications
JF  - American Journal of Embedded Systems and Applications
JO  - American Journal of Embedded Systems and Applications
SP  - 69
EP  - 74
PB  - Science Publishing Group
SN  - 2376-6085
UR  - https://doi.org/10.11648/j.ajesa.20180602.11
AB  - This paper is concerned with the adaptive impulsive synchronization for a class of delay fractional-order chaotic system. Firstly, according to the impulsive differential equations theory and the adaptive control theory, the adaptive impulsive controller and the parametric update law are designed, respectively. Secondly, by constructing the suitable response system, the original fractional-order error system can be converted into the integral-order one. Finally, based on the Lyapunov stability theory and the generalized Barbalat’s lemma, some new sufficient conditions are derived to guarantee the asymptotic stability of synchronization error system.
VL  - 6
IS  - 2
ER  -

Copy | Download