Analysis And Synchronization Control Based On Several Class Of Complex Networks

In recent years,complex networks have been widely used in many fields.The synchronization problem has attracted the attention of many scholars.Complex networks may cause changes in coupling strength or topological structure due to complex coupling relationships and huge network scales,which may cause the network to fail to achieve synchronization.Based on the consideration of key issues such as the structural characteristics of complex networks,synchronization control strategies,and applications in actual systems,the paper analyzes and discusses the synchronization control problems of several types of complex networks,taking into account random interference,adaptive coupling strength,and Markovian switching topological structure and other factors,using some control strategies such as nonfragile sampled-data control,non-fragile state feedback control,and event-triggered control,transform the synchronization problem of the complex network into the stability problem of the error system for analysis.The main research work is as follows:Firstly,a reliable additive non-fragile sampled-data control strategy is proposed to study synchronization problem for a class of complex networks with random disturbances and mixed coupling time delays.Based on the Lyapunov stability theory and stochastic differential theory,combined with the integral inequalities and the convex combination method,a sufficient condition is obtained such that complex networks can achieve synchronization.A numerical example verifies the effectiveness of the control strategy.Secondly,the synchronization problem of Markovian jump complex networks with nonlinear coupling relationship is analyzed.A multiplicative non-fragile controller is designed.By constructing a Lyapunov function based on time-varying delay,combining with integral inequalities,Lagrange median value theorem and so on,some sufficient conditions for the system to achieve synchronization and generalized dissipative are obtained.A numerical example verifies the effectiveness of the control strategy.Finally,the exponential synchronization problem of the Kuramoto oscillators model with adaptive coupling strength is studied,and an event-triggered control strategy is designed.According to the topological structure of the Kuramoto oscillators model,a Lyapunov function is constructed.Using the relevant knowledge of Lyapunov stability theory and graph theory,a sufficient condition for the Kuramoto oscillators model to achieve exponential synchronization is obtained.A numerical example verify the effectiveness of event-triggered control strategy.