Delay-Dependent Synchronization for Complex Dynamical Networks with Interval Time-Varying and Switched Coupling Delays
We investigate the local exponential synchronization for complex dynamical networks with interval time-varying delays in the dynamical nodes and the switched coupling term simultaneously. The constraint on the derivative of the time-varying delay is not required which allows the time delay to be a f...
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Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/367457 |
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| author | T. Botmart P. Niamsup |
| author_facet | T. Botmart P. Niamsup |
| author_sort | T. Botmart |
| collection | DOAJ |
| description | We investigate the local exponential synchronization for complex dynamical networks with
interval time-varying delays in the dynamical nodes and the switched coupling term simultaneously. The
constraint on the derivative of the time-varying delay is not required which allows the time delay to be
a fast time-varying function. By using common unitary matrix for different subnetworks, the problem of
synchronization is transformed into the stability analysis of some linear switched delay systems. Then, when
subnetworks are synchronizable and nonsynchronizable, a delay-dependent sufficient condition is derived
and formulated in the form of linear matrix inequalities (LMIs) by average dwell time approach and piecewise
Lyapunov-Krasovskii functionals which are constructed based on the descriptor model of the system and the
method of decomposition. The new stability condition is less conservative and is more general than some
existing results. A numerical example is also given to illustrate the effectiveness of the proposed method. |
| format | Article |
| id | doaj-art-4089649b70f74243af723f63412368a0 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-4089649b70f74243af723f63412368a02025-02-03T01:25:27ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/367457367457Delay-Dependent Synchronization for Complex Dynamical Networks with Interval Time-Varying and Switched Coupling DelaysT. Botmart0P. Niamsup1Department of Mathematics, Faculty of Science, Srinakharinwirot University, Bangkok 10110, ThailandCenter of Excellence in Mathematics CHE, Si Ayutthaya Road, Bangkok 10400, ThailandWe investigate the local exponential synchronization for complex dynamical networks with interval time-varying delays in the dynamical nodes and the switched coupling term simultaneously. The constraint on the derivative of the time-varying delay is not required which allows the time delay to be a fast time-varying function. By using common unitary matrix for different subnetworks, the problem of synchronization is transformed into the stability analysis of some linear switched delay systems. Then, when subnetworks are synchronizable and nonsynchronizable, a delay-dependent sufficient condition is derived and formulated in the form of linear matrix inequalities (LMIs) by average dwell time approach and piecewise Lyapunov-Krasovskii functionals which are constructed based on the descriptor model of the system and the method of decomposition. The new stability condition is less conservative and is more general than some existing results. A numerical example is also given to illustrate the effectiveness of the proposed method.http://dx.doi.org/10.1155/2013/367457 |
| spellingShingle | T. Botmart P. Niamsup Delay-Dependent Synchronization for Complex Dynamical Networks with Interval Time-Varying and Switched Coupling Delays Journal of Applied Mathematics |
| title | Delay-Dependent Synchronization for Complex Dynamical Networks with Interval Time-Varying and Switched Coupling Delays |
| title_full | Delay-Dependent Synchronization for Complex Dynamical Networks with Interval Time-Varying and Switched Coupling Delays |
| title_fullStr | Delay-Dependent Synchronization for Complex Dynamical Networks with Interval Time-Varying and Switched Coupling Delays |
| title_full_unstemmed | Delay-Dependent Synchronization for Complex Dynamical Networks with Interval Time-Varying and Switched Coupling Delays |
| title_short | Delay-Dependent Synchronization for Complex Dynamical Networks with Interval Time-Varying and Switched Coupling Delays |
| title_sort | delay dependent synchronization for complex dynamical networks with interval time varying and switched coupling delays |
| url | http://dx.doi.org/10.1155/2013/367457 |
| work_keys_str_mv | AT tbotmart delaydependentsynchronizationforcomplexdynamicalnetworkswithintervaltimevaryingandswitchedcouplingdelays AT pniamsup delaydependentsynchronizationforcomplexdynamicalnetworkswithintervaltimevaryingandswitchedcouplingdelays |