Exponential Synchronization Control Of Nonlinearly Coupled Complex Dynamical Networks With Time-varying Coupling Delays

In recent years,complex networks became a general research interest owing to the wide application in engineering,science,and society system.In fact,a variety of real-world systems,such as power grid system,financial networks,Internet,social networks,neural,food webs,traffic network and virus propagation network can be described by complex dynamical networks.Synchronization,which is a typical collective behavior of complex dynamical networks,has become active popular research topic.Based on this,this paper is summarized as follows:(1)Firstly,the exponential synchronization is studied for a class of uncertain complex dynamic networks with time-varying delay.The uncertainty satisfies the matching condition,the delay is unknown but bounded and in this paper.By constructing a suitable Lyapunov-Krasovskii function based on Lyapunov stability theory,using the linear matrix inequality(LMI)approach,and designing the appropriate feedback controllers,a new criterion of the exponential synchronization is derived.(2)It is necessary to consider whether complex networks can be synchronized,because it determines the necessity and feasibility of implementing the control function.Then based on this,we focuses on the global exponential synchronization problem of nonlinearly coupled complex dynamical networks with time-varying coupling delays.Several simple and generic global exponential synchronization criteria are derived based on the Lyapunov stability theory and the Dini derivatives using the Halanay and generalized Halanay inequalities.These criteria rely on system parameters alone and can be used conveniently in practical applications.In addition,the system parameters do not satisfy the conditions of the proposed criteria.That is,the system itself cannot synchronize.However,system synchronization can be achieved by adding the appropriate feedback controllers,thereby providing a practical and effective control method for complex dynamical networks.An estimation method of exponential convergence rate is also presented.(3)Finally,we investigates global exponential synchronization problem of a class of nonlinearly coupled complex dynamical networks with time-varying coupling delay by aperiodically intermittent feedback control.Considering time-varying coupling delayed network model and based on aperiodically intermittent control strategy,a proper feedback controller is designed for each control period.Through establishment of a new vector inequality based on Dini derivative,sufficient conditions are obtained to ensure global exponential synchronization of complex dynamic networks.