Exponential synchronization of the coupling delayed switching complex dynamical networks via impulsive control
- PDF / 344,005 Bytes
- 17 Pages / 595.28 x 793.7 pts Page_size
- 36 Downloads / 190 Views
RESEARCH
Open Access
Exponential synchronization of the coupling delayed switching complex dynamical networks via impulsive control Anding Dai1 , Wuneng Zhou1* , Jianwen Feng2 , Jian’an Fang1 and Shengbing Xu3 *
Correspondence: [email protected] 1 College of Computer Sciences and Technology, Donghua University, Shanghai, 201620, China Full list of author information is available at the end of the article
Abstract In this paper, we investigate the exponential synchronization issue of coupling delayed switching complex dynamical networks via impulsive control. Basing on the Lyapunov functional method and establishing a new impulsive delay differential inequality, we derive some sufficient conditions which depend on delay and impulses to guarantee the exponential synchronization of the coupling delay switching complex dynamical network. Finally, numerical simulations are given to illustrate the effectiveness of the obtained results. Keywords: exponential synchronization; complex dynamical network; switching topology; delayed coupling
1 Introduction During the last two decades, synchronization and control problems of complex dynamical networks have been focused on in many different fields such as mathematics, engineering, social and economic science, etc. [–]. Many effective methods, like feedback control, adaptive control, sampled-data control and impulsive control, are used to stabilize and synchronize a coupled complex dynamical network. At the same time, a wide variety of synchronization criteria have also been presented for different network coupling such as switch topology, time delays, impulsive characters, etc. Up to now, plenty of researchers have devoted much effort to guarantee synchronization of complex dynamical networks with fixed topology [–]. However, in real situations, many complex systems may be subject to abrupt changes in their connection structure or network mode switching caused by some phenomena such as link failures, component failures or repairs, changing subsystem interconnections, and abrupt environmental disturbance, etc. Although some synchronization criteria of networks with uncertain topological structure and continuous time-varying topology have been studied, those methods may not work for the network topology when it becomes discontinued or changes very quickly [, ]. Hence, to study the synchronization of the switched networks is still very useful and meaningful. Because of this reason, the synchronization of a complex network with switching topology has attracted researchers’ interest [–]. Wang et al. [] provided several synchronization criteria for switched networks, in which synchronization could be evaluated by the time average of the second smallest eigenvalue that corresponded to the Laplacians matrix of switching topology. Authors in [] studied the local and global expo© 2013 Dai et al.; licensee Springer. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits u
Data Loading...
