| Complex systems and networks have become a hot topic in network science and even control theory,which has attracted extensive attention of scholars in many fields.Complex networks often exhibit complex and interesting dynamic behaviors,including synchronization,consensus,clustering and other basic issues.Synchronization,a cluster behavior,has received widespread attention.Synchronization mechanism has been found to be a common phenomenon in nature,and has important potential applications in the dynamic system of the real world.Only a few complex dynamic networks can achieve synchronization by changing the characteristics of the system itself and the coupling strength of the network,while most complex networks need to achieve synchronization through external control inputs Therefore,the design of efficient controller has become a key issue in complex network synchronization.Among them,pulse control,as a typical discrete control method,is only activated when the pulse occurs.In many impulsive control or impulsive disturbance problems,the switching phenomenon of network state,the transient disturbance of frequency change or other sudden noises and sudden changes in some moments are inevitable,so different impulsive effects need to be considered.Lur’e system is a typical nonlinear system.Many common dynamic systems can be considered as Lur’e system to study.Therefore,the study of complex network model composed of Lur’e system coupling has great practical significance.This paper studies the global exponential synchronization of complex networks coupled by Lur’e system.By designing a reasonable impulse controller,the sufficient conditions for global exponential synchronization of networks are obtained,and the convergence rate of network synchronization is also concerned.The main work of this article is as follows.Firstly,this paper discusses the global exponential synchronization problem for a class of complex Lur’e networks with delays.For Lur’e complex networks with system delays,a suitable impulsive control strategy is designed to impose impulsive effects on the system in the network at the moment of the impulse.The concept of average pulse interval is introduced,and the synchronization conditions of the Lur’e complex network are obtained using flexible application of Kronecker product theory,generalized Lipschitz conditions,and analysis methods based on Halanay principle and non reference system strategy In addition,numerical simulation results demonstrate the effectiveness of the proposed synchronization theorem and control scheme.Secondly,this paper studies the global exponential synchronization problem of stochastic Lur’e delay coupled networks.For stochastic Lur’e time-delay coupled networks,a reasonable impulsive controller is designed to achieve global exponential synchronization for complex dynamic networks.Based on the comparison principle of impulsive systems and the analytical method of parametric variational method,sufficient conditions for achieving global exponential synchronization for this stochastic network are given In addition,a method for determining the synchronization of the network under both positive and negative pulse effects is also considered,and the convergence rates of the network under different pulse effects are given The simulation results verify the effectiveness of the derived conclusions and controller design.Finally,this paper discusses the global exponential synchronization problem for a class of dynamic networks coupled by Lur’e systems.For Lur’e networks with system delays,an effective controller is designed based on impulse control strategies.Based on the analysis methods of impulse interval iteration and Perron-Frobenius theorem,a criterion for achieving global exponential synchronization for coupled Lur’e networks with time-varying delays is proposed,and an estimate of the convergence rate for achieving global exponential synchronization for the network is given In addition,the numerical simulation results show the effectiveness of the obtained results. |
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