Synchronization Criteria For Complex Dynamical Networks With Time-varying Delays

In recent years,complex networks have gradually become the focus of studies.It has relationship with many science and engineering fields.As a collective property of the complex networks,the synchronization in networks is valuable for industry and life in many examples,so it is the main problem that how to control the dynamical networks.Of course,many researchers have discussed this problem,and they have got some useful results.But there are many problems remain unsolved.For example,in a control processing,people usually think that the less connecting nods selected,the better(compared with all nods in the network).but this kind of control strategy is not the one which cost the least resource.This is a problem worth thinking.Another problem is that the network discussed is constant,but in fact most networks are increasing.In another words,the nods of the complex network are increasing all the time.Meanwhile,many networks in reality have time delays,and most of them have time-varying delays.Therefore with the researching on time-varying delayed networks,we can get a better understanding of the dynamic behavior of network in reality.In view of the above questions,in this piper,we firstly discussed several synchronization control problems in complex network with time-varying delays, applied local feedback injections to a fraction of network nodes,and got some criteria about the we discussed synchronization of the complex networks and got some criteria about the synchronization of the complex networks.In the section three and section four we mainly studied three kinds of dynamical networks models with time-varying delays and got some criteria in synchronization of complex dynamical networks by employed Lyapunov functional method.The paper applies knowledge related to control theory,matrix inequality,matrix measure the stability and linearization partly to solve the synchronization of the complex networks.By the research the complex dynamical networks with time-varying delays,we can understand and explain some dynamic characters of complex network.At the same time,the result can give reference to certain control of network in reality.