Abstract and Applied Analysis

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

Seng-Kin Lao, Lap-Mou Tam, Hsien-Keng Chen, and Long-Jye Sheu

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Abstract

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.

Article information

Source
Abstr. Appl. Anal., Volume 2014 (2014), Article ID 316368, 11 pages.

Dates
First available in Project Euclid: 2 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412273297

Digital Object Identifier
doi:10.1155/2014/316368

Mathematical Reviews number (MathSciNet)
MR3193499

Zentralblatt MATH identifier
07022155

Citation

Lao, Seng-Kin; Tam, Lap-Mou; Chen, Hsien-Keng; Sheu, Long-Jye. Hybrid Stability Checking Method for Synchronization of Chaotic Fractional-Order Systems. Abstr. Appl. Anal. 2014 (2014), Article ID 316368, 11 pages. doi:10.1155/2014/316368. https://projecteuclid.org/euclid.aaa/1412273297


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