Robust Synchronization of Uncertain Fractional Order Chaotic Systems

Junhai LUO  Heng LIU  Jiangfeng YANG  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E98-A   No.10   pp.2109-2116
Publication Date: 2015/10/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E98.A.2109
Type of Manuscript: PAPER
Category: Systems and Control
fractional order chaotic system,  synchronization,  robust control,  fractional-order Lyapunov director method,  

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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.