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

Author

Listed:
  • Seng-Kin Lao
  • Lap-Mou Tam
  • Hsien-Keng Chen
  • Long-Jye Sheu

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.

Suggested Citation

  • Seng-Kin Lao & Lap-Mou Tam & Hsien-Keng Chen & Long-Jye Sheu, 2014. "Hybrid Stability Checking Method for Synchronization of Chaotic Fractional‐Order Systems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:316368
    DOI: 10.1155/2014/316368
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    References listed on IDEAS

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    1. Xiaobing Zhou & Lianglin Xiong & Weiwei Cai & Xiaomei Cai, 2013. "Adaptive Synchronization and Antisynchronization of a Hyperchaotic Complex Chen System with Unknown Parameters Based on Passive Control," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-8, March.
    2. Fahd Jarad & Thabet Abdeljawad & Dumitru Baleanu & Kübra Biçen, 2012. "On the Stability of Some Discrete Fractional Nonautonomous Systems," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-9, February.
    3. Xiaobing Zhou & Lianglin Xiong & Weiwei Cai & Xiaomei Cai, 2013. "Adaptive Synchronization and Antisynchronization of a Hyperchaotic Complex Chen System with Unknown Parameters Based on Passive Control," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    4. Fahd Jarad & Thabet Abdeljawad & Dumitru Baleanu & Kübra Biçen, 2012. "On the Stability of Some Discrete Fractional Nonautonomous Systems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
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