Synchronization Analysis Of Complex-Valued Chaotic Lur'e System

As we all know,complex-valued complex networks(CVCNs)are an extended for-m of real-valued complex networks(RVCNs),which have potential applications in laser systems,symmetry detection,thermal convection systems and XOR symmetry prob-lems.CVCNs can handle some problems that RVCNs cannot handle,such as XOR problems.Lur'e system has a wide range of representative meanings in chaotic systems,so it is very valuable to study it.In the process of studying the Lur'e system,time delay is a factor that should be considered.Time delay not only leads to poor performance,but also makes the system become unstable.In summary,due to these factors,it is of great significance to study the master-slave synchronization problem of complex-valued chaotic Lur'e systems(CVCLSs)with time delays.This thesis mainly studies the syn-chronization of two types of CVCLSs with time delays.Using linear matrix inequality,Lyapunov stability theory and control theory,the master-slave system's global synchro-nization is realized.The main work of this thesis is as follows:In the first chapter,we introduce the background knowledge of chaotic Lur'e sys-tems,the general development of chaotic systems and the research status of Lur'e sys-tems and complex neural networks.The master-slave synchronization problem of a class of CVCLSs with discrete time delays is discussed in the second chapter.In order to simplify the calculation process,a method of converting the complex-value system into two real-value systems is adopted.Based on the linear matrix inequality and the Lyapunov stability theory,the sufficient conditions for the synchronization of the master-slave system are derived.What's more,a conclusion is derived that is applicable to the complex-valued Lur'e systems without discrete time delay.In the third chapter,we study the global exponential stability of a class of neutral CVCLSs with time-varying delays.Firstly,CVCLSs are converted to corresponding RV-CLSs.Secondly,based on an appropriate impulse control law,the appropriate Lyapunov function is constructed.A sufficient criterion to ensure the global exponential stability of the system is obtained by using the matrix inequality theory and Lyapunov stability theory.Finally,we discuss the shortcomings of the thesis and the direction of future re-search in the fourth chapter.