Synchronization Criteria Of Complex Systems Based On Several Classes Of Control Approaches

With the rapid development of complex network in recent years,the synchronization control problem of complex systems has become a research hot spot in the field of control.Designing appropriate controller is one of the most basic methods to achieve synchronization of complex systems.Many scholars have proposed different control strategies.It is found that the quantitative control and nonlinear feedback control are used to study the synchronization properties of complex systems,and the results reduce the dependence on coupling strength in the control process and solve the nonlinear problems in the synchronous control process.In addition,the design complexity of linear matrix inequality method can be reduced by introducing M-cone method to study the synchronization of complex systems.Therefore,it is of great theoretical value and practical significance to study the synchronization of complex systems by using the above methods.However,the above methods have not been paid enough attention in the study of synchronization control of complex systems.This paper introduces several control methods to study the complete synchronization,ψ-type synchronization and impulsive synchronization of complex systems on the basis of existing achievements.Based on different control methods,this paper analyzes the synchronization of several kinds of complex systems: in the first part,the complete synchronization of chaotic systems is discussed.By using comparison theorem and Lyapunov stability theory,designing the switch periodic static logarithmic quantization controller and the average time coupling strength,the synchronization criterion of the system state reaching global exponential stability is established,which reveals the internal law of the quantization effect and the average time coupling strength and the system synchronization.In the second part,by designing nonlinear feedback controller and corresponding Lyapunov function,using differential inclusion theory and some lemmas,the synchronization criterion of the network under the action of the controller is obtained,and the existing nonlinear problems are solved.At the same time,it is shown that the network synchronization is carried out in a general framework,and the results are more general.In the third part,the synchronization of memristive delayed neural networks is studied.By designing mixed impulsive delayed controller,the properties of M-cone,differential inclusion theory and some lemmas,where given to consider the influence of initial condition and time delay on the system,new criteria of network synchronization were obtained.In the process of synchronous analysis,it is found that the M-cone method can reduce the design complexity based on linear matrix inequality.