%0 Journal Article
%T Pinning Stabilization of Complex Networks Coupled with Time Delay and Disturbed with Stochastic Noise
%A Chun-Xia Fan
%A Yu Gu
%A Qingyang Wei
%J Journal of Control Science and Engineering
%D 2014
%I Hindawi Publishing Corporation
%R 10.1155/2014/489049
%X A pinning stabilization problem of complex networks with time-delay coupling is studied under stochastic noisy circumstances in this paper. Only one controller is used to stabilize the network to the equilibrium point when the network is connected and the minimal number of controllers is used when the network is unconnected, where the structure of complex network is fully used. Some criteria are achieved to control the complex network under stochastic noise in the form of linear matrix inequalities. Several examples are given to show the validity of the proposed control criteria. 1. Introduction Complex networks have been a major research topic and attracted increasing attention from various fields including physics, biology, sociology, and engineering. Many real phenomena can be described as complex networks, such as the World Web, telephone call graphs, and social organization. Recently, the stabilization and synchronization problem and stabilization problem of complex network have become more and more important. In fact, the synchronization problem is a special stabilization one since it can be converted into the stabilization problem of the error system between the complex network and the synchronization manifold [1¨C3]. Specially, the synchronization problem is a stabilization one when the synchronization manifold is an equilibrium orbit. So in this paper, we study the stabilization problem of complex networks which can be extended to the synchronization problem. Many contributions on complex network synchronization or stabilization are derived on the basis of the inner coupling strength adjustable [4¨C6]; that is, the whole network can synchronize or stabilize by itself. However, it is true that the inner coupling strength sometimes cannot be adjustable for a complex network. Consequently, the whole network cannot be synchronized or stabilized by itself [7]. Therefore, some additional controllers have to be applied to force the network to be synchronized or stabilized. How many controllers are added to stabilize the complex network? Adding the controllers to all the nodes is the most simple but costly and impossible due to the complexity of network. To reduce the number of controlled nodes, some local feedback injections are applied to a fraction of networks nodes, which is called pinning control [8¨C12]. Wang and Chen found that specific pinning of the nodes with larger degree required a smaller number of controlled nodes than the random pinning for a scale-free network [8]. Li et al. proposed the virtual control method for microscopic dynamics
%U http://www.hindawi.com/journals/jcse/2014/489049/