Physics Letters A 372 (2008) 1601–1606 www.elsevier.com/locate/pla Adaptive–impulsive synchronization of uncertain complex dynamical networks K. Li a,c,∗ , C.H. Lai b,c a Temasek Laboratories, National University of Singapore, Singapore 117508, Singapore b Department of Physics, National University of Singapore, Singapore 117542, Singapore c Beijing-Hong Kong-Singapore Joint Center of Nonlinear & Complex systems (Singapore), National University of Singapore, Kent Ridge, Singapore 119260, Singapore Received 15 March 2007; received in revised form 21 September 2007; accepted 4 October 2007 Available online 9 October 2007 Communicated by A.R. Bishop Abstract This Letter studies adaptive–impulsive synchronization of uncertain complex dynamical networks. Based on the stability analysis of impulsive system, several network synchronization criteria for local and global adaptive–impulsive synchronization are established. Numerical example is also given to illustrate the results.  2007 Elsevier B.V. All rights reserved. PACS: 05.45.Gg Keywords: Adaptive–impulsive control; Uncertain dynamical networks; Synchronization 1. Introduction Recently, complex dynamical networks have attracted a great deal of attentions. One of the interesting phenomena in complex dynamical networks is the synchronization of all dy- namical nodes in the network [1–9]. Most of the existing works on synchronization of complex networks consider a given net- work, that is, the dynamical of each node and coupling func- tions are known [2–5]. However, in practice, it is often difficult to get the exact estimation of the coupling strength. And we have little information about the network structure. On the other hand, it is also noticed that in these schemes the final state of the network, where the network will reach after achieving syn- chronization, is usually not known in advance and cannot be changed as design [8]. Therefore, it would be interesting to study a general situation where the network coupling is un- known but bounded linear/nonlinear function, and the network * Corresponding author at: Temasek Laboratories, National University of Sin- gapore, Singapore 117508, Singapore. E-mail address: tsllk@nus.edu.sg (K. Li). structure is only partially known or completely unknown a pri- ori. And it is desirable if the state that the network will synchro- nize to can be chosen. In this Letter, we study the synchronization of uncertain dy- namical networks, and propose an adaptive–impulsive synchro- nization approach for uncertain complex dynamical networks. Based on the comparison theorem for the stability of impulsive control system developed in [11], several network synchro- nization criteria are established. We design robust adaptive– impulsive controllers which can ensure that the states of the dy- namical network locally or globally asymptotically synchronize with an arbitrarily assigned state of an isolate node of the net- work. In comparison with the results of the adaptive-feedback approach [9,10], the proposed scheme has faster convergence rate and smaller final coupling strength. In addition, network could be synchronized in larger impulsive distance compare to ordinary impulsive synchronization schemes [6,7]. This Letter is organized as follows. In Section 2, we first de- scribe the general uncertain complex dynamical model and for- mulate the problem of adaptive–impulsive synchronization for an uncertain dynamical network. In Section 3, local and global 0375-9601/$ – see front matter  2007 Elsevier B.V. All rights reserved. doi:10.1016/j.physleta.2007.10.020