Pinning Synchronization for Complex Networks with Interval Coupling Delay by Variable Subintervals Method and Finsler’s Lemma
The pinning synchronous problem for complex networks with interval delays is studied in this paper. First, by using an inequality which is introduced from Newton-Leibniz formula, a new synchronization criterion is derived. Second, combining Finsler’s Lemma with homogenous matrix, convergent linear m...
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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2017/2137103 |
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| author | Dawei Gong Frank L. Lewis Liping Wang Dong Dai Shuang Zhang |
| author_facet | Dawei Gong Frank L. Lewis Liping Wang Dong Dai Shuang Zhang |
| author_sort | Dawei Gong |
| collection | DOAJ |
| description | The pinning synchronous problem for complex networks with interval delays is studied in this paper. First, by using an inequality which is introduced from Newton-Leibniz formula, a new synchronization criterion is derived. Second, combining Finsler’s Lemma with homogenous matrix, convergent linear matrix inequality (LMI) relaxations for synchronization analysis are proposed with matrix-valued coefficients. Third, a new variable subintervals method is applied to expand the obtained results. Different from previous results, the interval delays are divided into some subdelays, which can introduce more free weighting matrices. Fourth, the results are shown as LMI, which can be easily analyzed or tested. Finally, the stability of the networks is proved via Lyapunov’s stability theorem, and the simulation of the trajectory claims the practicality of the proposed pinning control. |
| format | Article |
| id | doaj-art-1d30b811c5e4487087b8069bd133928b |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-1d30b811c5e4487087b8069bd133928b2025-02-03T01:07:02ZengWileyComplexity1076-27871099-05262017-01-01201710.1155/2017/21371032137103Pinning Synchronization for Complex Networks with Interval Coupling Delay by Variable Subintervals Method and Finsler’s LemmaDawei Gong0Frank L. Lewis1Liping Wang2Dong Dai3Shuang Zhang4School of Mechatronics Engineering, University of Electronic Science and Technology of China, Chengdu 611731, ChinaUTA Research Institute, The University of Texas at Arlington, Arlington, TX 76118, USADepartment of Mechanical Engineering, Tsinghua University, Beijing 100084, ChinaSchool of Electric Power, South China University of Technology, Guangzhou 510641, ChinaSchool of Astronautics and Aeronautic, University of Electronic Science and Technology of China, Chengdu 611731, ChinaThe pinning synchronous problem for complex networks with interval delays is studied in this paper. First, by using an inequality which is introduced from Newton-Leibniz formula, a new synchronization criterion is derived. Second, combining Finsler’s Lemma with homogenous matrix, convergent linear matrix inequality (LMI) relaxations for synchronization analysis are proposed with matrix-valued coefficients. Third, a new variable subintervals method is applied to expand the obtained results. Different from previous results, the interval delays are divided into some subdelays, which can introduce more free weighting matrices. Fourth, the results are shown as LMI, which can be easily analyzed or tested. Finally, the stability of the networks is proved via Lyapunov’s stability theorem, and the simulation of the trajectory claims the practicality of the proposed pinning control.http://dx.doi.org/10.1155/2017/2137103 |
| spellingShingle | Dawei Gong Frank L. Lewis Liping Wang Dong Dai Shuang Zhang Pinning Synchronization for Complex Networks with Interval Coupling Delay by Variable Subintervals Method and Finsler’s Lemma Complexity |
| title | Pinning Synchronization for Complex Networks with Interval Coupling Delay by Variable Subintervals Method and Finsler’s Lemma |
| title_full | Pinning Synchronization for Complex Networks with Interval Coupling Delay by Variable Subintervals Method and Finsler’s Lemma |
| title_fullStr | Pinning Synchronization for Complex Networks with Interval Coupling Delay by Variable Subintervals Method and Finsler’s Lemma |
| title_full_unstemmed | Pinning Synchronization for Complex Networks with Interval Coupling Delay by Variable Subintervals Method and Finsler’s Lemma |
| title_short | Pinning Synchronization for Complex Networks with Interval Coupling Delay by Variable Subintervals Method and Finsler’s Lemma |
| title_sort | pinning synchronization for complex networks with interval coupling delay by variable subintervals method and finsler s lemma |
| url | http://dx.doi.org/10.1155/2017/2137103 |
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