Hybrid Stability Checking Method for Synchronization of Chaotic Fractional-Order Systems
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...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/316368 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832559098971815936 |
|---|---|
| author | Seng-Kin Lao Lap-Mou Tam Hsien-Keng Chen Long-Jye Sheu |
| author_facet | Seng-Kin Lao Lap-Mou Tam Hsien-Keng Chen Long-Jye Sheu |
| author_sort | Seng-Kin Lao |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-c841fa17ed6843de974eda041b880333 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-c841fa17ed6843de974eda041b8803332025-02-03T01:30:56ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/316368316368Hybrid Stability Checking Method for Synchronization of Chaotic Fractional-Order SystemsSeng-Kin Lao0Lap-Mou Tam1Hsien-Keng Chen2Long-Jye Sheu3Department of Electromechanical Engineering, Faculty of Science and Technology, University of Macau, Avenue Padre Tomás Pereira, Taipa 999078, MacauDepartment of Electromechanical Engineering, Faculty of Science and Technology, University of Macau, Avenue Padre Tomás Pereira, Taipa 999078, MacauDepartment of Mechanical Engineering, Hsiuping University of Science and Technology, 11 Gongye Road, Dali District, Taichung 412-80, TaiwanDepartment of Mechanical Engineering, Chung Hua University, Section 2, 707 WuFu Road, Hsinchu 30012, TaiwanA 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.http://dx.doi.org/10.1155/2014/316368 |
| spellingShingle | Seng-Kin Lao Lap-Mou Tam Hsien-Keng Chen Long-Jye Sheu Hybrid Stability Checking Method for Synchronization of Chaotic Fractional-Order Systems Abstract and Applied Analysis |
| title | Hybrid Stability Checking Method for Synchronization of Chaotic Fractional-Order Systems |
| title_full | Hybrid Stability Checking Method for Synchronization of Chaotic Fractional-Order Systems |
| title_fullStr | Hybrid Stability Checking Method for Synchronization of Chaotic Fractional-Order Systems |
| title_full_unstemmed | Hybrid Stability Checking Method for Synchronization of Chaotic Fractional-Order Systems |
| title_short | Hybrid Stability Checking Method for Synchronization of Chaotic Fractional-Order Systems |
| title_sort | hybrid stability checking method for synchronization of chaotic fractional order systems |
| url | http://dx.doi.org/10.1155/2014/316368 |
| work_keys_str_mv | AT sengkinlao hybridstabilitycheckingmethodforsynchronizationofchaoticfractionalordersystems AT lapmoutam hybridstabilitycheckingmethodforsynchronizationofchaoticfractionalordersystems AT hsienkengchen hybridstabilitycheckingmethodforsynchronizationofchaoticfractionalordersystems AT longjyesheu hybridstabilitycheckingmethodforsynchronizationofchaoticfractionalordersystems |