Synchronization of General Complex Networks with Hybrid Couplings and Unknown Perturbations
The issue of synchronization for a class of hybrid coupled complex networks with mixed delays (discrete delays and distributed delays) and unknown nonstochastic external perturbations is studied. The perturbations do not disappear even after all the dynamical nodes have reached synchronization. To o...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/625372 |
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| _version_ | 1832552792977309696 |
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| author | Xinsong Yang Shuang Ai Tingting Su Ancheng Chang |
| author_facet | Xinsong Yang Shuang Ai Tingting Su Ancheng Chang |
| author_sort | Xinsong Yang |
| collection | DOAJ |
| description | The issue of synchronization for a class of hybrid coupled complex networks with mixed delays (discrete delays and distributed delays) and unknown nonstochastic external perturbations is studied. The perturbations do not disappear even after all the dynamical nodes have reached synchronization. To overcome the bad effects of such perturbations, a simple but all-powerful robust adaptive controller is designed to synchronize the complex networks even without knowing a priori the functions and bounds of the perturbations. Based on Lyapunov stability theory, integral inequality Barbalat lemma, and Schur Complement lemma, rigorous proofs are given for synchronization of the complex networks. Numerical simulations verify the effectiveness of the new robust adaptive controller. |
| format | Article |
| id | doaj-art-95679bc7cbbe4f499247b26678880518 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-95679bc7cbbe4f499247b266788805182025-02-03T05:57:53ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/625372625372Synchronization of General Complex Networks with Hybrid Couplings and Unknown PerturbationsXinsong Yang0Shuang Ai1Tingting Su2Ancheng Chang3Department of Mathematics, Chongqing Normal University, Chongqing 400047, ChinaDepartment of Mathematics, Chongqing Normal University, Chongqing 400047, ChinaDepartment of Mathematics, Chongqing Normal University, Chongqing 400047, ChinaDepartment of Mathematics, Hunan Information Science Vocational College, Changsha, Hunan 410151, ChinaThe issue of synchronization for a class of hybrid coupled complex networks with mixed delays (discrete delays and distributed delays) and unknown nonstochastic external perturbations is studied. The perturbations do not disappear even after all the dynamical nodes have reached synchronization. To overcome the bad effects of such perturbations, a simple but all-powerful robust adaptive controller is designed to synchronize the complex networks even without knowing a priori the functions and bounds of the perturbations. Based on Lyapunov stability theory, integral inequality Barbalat lemma, and Schur Complement lemma, rigorous proofs are given for synchronization of the complex networks. Numerical simulations verify the effectiveness of the new robust adaptive controller.http://dx.doi.org/10.1155/2013/625372 |
| spellingShingle | Xinsong Yang Shuang Ai Tingting Su Ancheng Chang Synchronization of General Complex Networks with Hybrid Couplings and Unknown Perturbations Abstract and Applied Analysis |
| title | Synchronization of General Complex Networks with Hybrid Couplings and Unknown Perturbations |
| title_full | Synchronization of General Complex Networks with Hybrid Couplings and Unknown Perturbations |
| title_fullStr | Synchronization of General Complex Networks with Hybrid Couplings and Unknown Perturbations |
| title_full_unstemmed | Synchronization of General Complex Networks with Hybrid Couplings and Unknown Perturbations |
| title_short | Synchronization of General Complex Networks with Hybrid Couplings and Unknown Perturbations |
| title_sort | synchronization of general complex networks with hybrid couplings and unknown perturbations |
| url | http://dx.doi.org/10.1155/2013/625372 |
| work_keys_str_mv | AT xinsongyang synchronizationofgeneralcomplexnetworkswithhybridcouplingsandunknownperturbations AT shuangai synchronizationofgeneralcomplexnetworkswithhybridcouplingsandunknownperturbations AT tingtingsu synchronizationofgeneralcomplexnetworkswithhybridcouplingsandunknownperturbations AT anchengchang synchronizationofgeneralcomplexnetworkswithhybridcouplingsandunknownperturbations |