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Complexity
Volume 2017 (2017), Article ID 2137103, 9 pages
https://doi.org/10.1155/2017/2137103
Research Article

Pinning Synchronization for Complex Networks with Interval Coupling Delay by Variable Subintervals Method and Finsler’s Lemma

1School of Mechatronics Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China
2UTA Research Institute, The University of Texas at Arlington, Arlington, TX 76118, USA
3Northeastern University, Shenyang 110036, China
4Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China
5School of Electric Power, South China University of Technology, Guangzhou 510641, China
6School of Astronautics and Aeronautic, University of Electronic Science and Technology of China, Chengdu 611731, China

Correspondence should be addressed to Dawei Gong; moc.621@xhzhzp

Received 18 March 2017; Accepted 4 May 2017; Published 8 June 2017

Academic Editor: Junpei Zhong

Copyright © 2017 Dawei Gong et al. 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.

Abstract

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.