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Abstract and Applied Analysis
Volume 2014, Article ID 316368, 11 pages
Research Article

Hybrid Stability Checking Method for Synchronization of Chaotic Fractional-Order Systems

1Department of Electromechanical Engineering, Faculty of Science and Technology, University of Macau, Avenue Padre Tomás Pereira, Taipa 999078, Macau
2Institute for the Development and Quality, Avenue Padre Tomás Pereira, Taipa 999078, Macau
3Department of Mechanical Engineering, Hsiuping University of Science and Technology, 11 Gongye Road, Dali District, Taichung 412-80, Taiwan
4Department of Mechanical Engineering, Chung Hua University, Section 2, 707 WuFu Road, Hsinchu 30012, Taiwan

Received 24 October 2013; Accepted 28 February 2014; Published 3 April 2014

Academic Editor: Dumitru Baleanu

Copyright © 2014 Seng-Kin Lao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A hybrid stability checking method is proposed to verify the establishment of synchronization between two hyperchaotic systems. During the design stage of a synchronization scheme for chaotic fractional-order systems, a problem is sometimes encountered. In order to ensure the stability of the error signal between two fractional-order systems, the arguments of all eigenvalues of the Jacobian matrix of the erroneous system should be within a region defined in Matignon’s theorem. Sometimes, the arguments depend on the state variables of the driving system, which makes it difficult to prove the stability. We propose a new and efficient hybrid method to verify the stability in this situation. The passivity-based control scheme for synchronization of two hyperchaotic fractional-order Chen-Lee systems is provided as an example. Theoretical analysis of the proposed method is validated by numerical simulation in time domain and examined in frequency domain via electronic circuits.