Eur. Phys. J. B (2013) 86: 125
https://doi.org/10.1140/epjb/e2013-30517-6

Regular Article

Exponentially asymptotic synchronization of uncertain complex time-delay dynamical networks

¹ Information Security Center, State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, P.O. Box 145, Beijing 100876, P.R. China
² Potsdam Institute for Climate Impact Research, 14473 Potsdam, Germany
³ National Engineering Laboratory for Disaster Backup and Recovery, Beijing University of Posts and Telecommunications, Beijing 100876, P.R. China

^a e-mail: lilixiang2006@yahoo.com.cn

Received: 27 June 2012
Received in final form: 17 January 2013
Published online: 1 April 2013

Abstract

This paper investigates the problem of exponentially asymptotic synchronization of complex time-delay dynamical networks with multi-links and structure uncertainty. The structure uncertainty belongs to the uncertain coupling strength and unknown topologies structures, which appear typically in networks environment. In order to synchronize complex networks with structure uncertainty, the adaptive controller is designed, and some general synchronization criteria of the controllers are proposed and proved based on the Lyapunov stability theory and the Lipschitz hypothesis. Finally, numerical simulations of dynamical networks with different topological structures are presented to demonstrate the feasibility and the effectiveness of the results.