Research On Synchronization Of Complex Delayed Networks System Based On Control Methods

At the end of the twentieth century,human society gradually entered the network age with the rapid development of information technology.In real life,many complex systems can be described by complex networks,such as Internet network,the world wide web(WWW),gene regulatory networks,scientific collaboration network and railway network,thus the complex networks system is closely related to our daily lives.With the in-depth study of complex networks system theory and its applications,complex network has penetrated into all fields of biological science,mathematical science and engineering science,and it becomes a new research topic to research complex networks system.In fact,time delay is an inevitable phenomenon in signal transmission of complex network systems,time delays will increase the instability and complexity of network systems.Therefore,it is possible to describe the nature of the entire network more accurately by considering the dynamic behavior of complex networks with time delays.As one of the typical collective behavior in complex network systems,synchronization behaviours vastly exist in different complex network systems.Accordingly,there are very important theoretical value and practical significance to study the synchronization and control problems of time-delay complex network systems.The main contents of this paper are as follows:(1)First,we considered a class of complex network models with time-varying delays.Based on the Lyapunov stability theory,Kronecker product property and linear matrix inequality method,we got the judgement basis of synchronization in finite time under the action of adaptive controller.A numerical example is given at the end of this chapter,and through the simulation results demonstrate the effectiveness of the proposed method.(2)In this chapter,we investigated the exponential synchronization problem of Markov jump complex time-delay network systems.Based on the given network model,we obtained several conditions for mean square exponential synchronization of this network systems by using Lyapunov stability theory and feedback control theory.The simulation results of the final numerical example proved the effectiveness and feasibility of the proposed approach.(3)For a class of complex network systems with time-varying delay and distribution delay,we studied synchronization conditions of the system under the influence of stochastic disturbance.First,it is easy to get the synchronization error equations of the systems by using adaptive sliding mode control.Based on this,the linear matrix inequality method and other basic theoretical knowledge were applied to synchronize this kind of stochastic complex time-delay network systems can be synchronized.At the end of this chapter,a numerical simulation example was presented to verify the validity of the presented results.Finally,the work of this paper is summarized,and the future research work is prospected.