Journal of Applied Mathematics
Volume 2013 (2013), Article ID 367457, 16 pages
Research Article

Delay-Dependent Synchronization for Complex Dynamical Networks with Interval Time-Varying and Switched Coupling Delays

T. Botmart1,2 and P. Niamsup2,3,4

1Department of Mathematics, Faculty of Science, Srinakharinwirot University, Bangkok 10110, Thailand
2Center of Excellence in Mathematics CHE, Si Ayutthaya Road, Bangkok 10400, Thailand
3Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
4Materials Science Research Center, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand

Received 29 December 2012; Accepted 31 January 2013

Academic Editor: Xinzhi Liu

Copyright © 2013 T. Botmart and P. Niamsup. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.