Mechanism of synchronization in switched nonlinear coupled dynamic networks

¹ Department of Automatic Control Engineering and Centre for Complex Systems, Xidian University Xi'an 710071, China
² Intelligence and communications for Robots Laboratory, Division of Computer Science and Engineering, Hanyang University - 17 Haengdang-dong, Seongdong-gu, 133-791, Seoul, Republic of Korea
³ State Key Laboratory for Turbulence and Complex Systems, Center for Systems and Control, College of Engineering, Peking University - Beijing 100871, China

^a zhli@xidian.edu.cn ; zhilih@hotmail.com
^b ihsuh@hanyang.ac.kr
^c longwang@pku.edu.cn

Received: 22 January 2010
Accepted: 11 August 2010

Abstract

In this letter, by constructing a switching symmetric matrix, we derive a criterion of exponential synchronization stability in a switched nonlinear coupled dynamical network. This criterion reveals that the mechanism of the synchronization stability is the largest eigenvalue of the switching symmetric matrix and the largest switching coupling strength. We analyze the feasibility of the proposed criterion with the eigenvalue-based method and the diagonally dominant property of the matrices, respectively. And meanwhile, we give the threshold of the switching coupling strength. Unlike other existing results, the deduction processes of our main results are based on the original synchronization stability definition rather than any introduced disagreement function. Besides, the proposed synchronization stability algorithm can be used conveniently.