Robust Synchronization of Uncertain Fractional Order Chaotic Systems

Junhai LUO; Heng LIU; Jiangfeng YANG

doi:10.1587/transfun.E98.A.2109

Robust Synchronization of Uncertain Fractional Order Chaotic Systems

Junhai LUO, Heng LIU, Jiangfeng YANG

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In this paper, synchronization for uncertain fractional order chaotic systems is investigated. By using the fractional order extension of the Lyapunov stability criterion, a linear feedback controller and an adaptive controller are designed for synchronizing uncertain fractional order chaotic systems without and with unknown external disturbance, respectively. Quadratic Lyapunov functions are used in the stability analysis of fractional-order systems, and fractional order adaptation law is constructed to update design parameter. The proposed methods can guarantee that the synchronization error converges to zero asymptotically. Finally, illustrative examples are given to confirm the theoretical results.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E98-A No.10 pp.2109-2116

Publication Date: 2015/10/01

Publicized

Online ISSN: 1745-1337

DOI: 10.1587/transfun.E98.A.2109

Type of Manuscript: PAPER

Category: Systems and Control

Authors

Junhai LUO
  University of Electronic Scienceand Technology of China
Heng LIU
  Shaanxi Normal University
Jiangfeng YANG
  University of Electronic Scienceand Technology of China

Keyword

fractional order chaotic system, synchronization, robust control, fractional-order Lyapunov director method

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Junhai LUO, Heng LIU, Jiangfeng YANG, "Robust Synchronization of Uncertain Fractional Order Chaotic Systems" in IEICE TRANSACTIONS on Fundamentals, vol. E98-A, no. 10, pp. 2109-2116, October 2015, doi: 10.1587/transfun.E98.A.2109.
Abstract: In this paper, synchronization for uncertain fractional order chaotic systems is investigated. By using the fractional order extension of the Lyapunov stability criterion, a linear feedback controller and an adaptive controller are designed for synchronizing uncertain fractional order chaotic systems without and with unknown external disturbance, respectively. Quadratic Lyapunov functions are used in the stability analysis of fractional-order systems, and fractional order adaptation law is constructed to update design parameter. The proposed methods can guarantee that the synchronization error converges to zero asymptotically. Finally, illustrative examples are given to confirm the theoretical results.
URL: https://globals.ieice.org/en_transactions/fundamentals/10.1587/transfun.E98.A.2109/_p

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@ARTICLE{e98-a_10_2109,
author={Junhai LUO, Heng LIU, Jiangfeng YANG, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Robust Synchronization of Uncertain Fractional Order Chaotic Systems},
year={2015},
volume={E98-A},
number={10},
pages={2109-2116},
abstract={In this paper, synchronization for uncertain fractional order chaotic systems is investigated. By using the fractional order extension of the Lyapunov stability criterion, a linear feedback controller and an adaptive controller are designed for synchronizing uncertain fractional order chaotic systems without and with unknown external disturbance, respectively. Quadratic Lyapunov functions are used in the stability analysis of fractional-order systems, and fractional order adaptation law is constructed to update design parameter. The proposed methods can guarantee that the synchronization error converges to zero asymptotically. Finally, illustrative examples are given to confirm the theoretical results.},
keywords={},
doi={10.1587/transfun.E98.A.2109},
ISSN={1745-1337},
month={October},}

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TY - JOUR
TI - Robust Synchronization of Uncertain Fractional Order Chaotic Systems
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2109
EP - 2116
AU - Junhai LUO
AU - Heng LIU
AU - Jiangfeng YANG
PY - 2015
DO - 10.1587/transfun.E98.A.2109
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E98-A
IS - 10
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - October 2015
AB - In this paper, synchronization for uncertain fractional order chaotic systems is investigated. By using the fractional order extension of the Lyapunov stability criterion, a linear feedback controller and an adaptive controller are designed for synchronizing uncertain fractional order chaotic systems without and with unknown external disturbance, respectively. Quadratic Lyapunov functions are used in the stability analysis of fractional-order systems, and fractional order adaptation law is constructed to update design parameter. The proposed methods can guarantee that the synchronization error converges to zero asymptotically. Finally, illustrative examples are given to confirm the theoretical results.
ER -