## Abstract and Applied Analysis

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

#### 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

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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