Research On Sampling Control And Synchronization Of Complex Variable Networks

Synchronization and control of dynamical networks is always a hot topic in complexity science.Researchers have proposed many control schemes for studying the synchronization problem of different network models.Sample control needs the observed data only at a sequence of instants.Therefore,it has been widely adopted due to its advantages of easier implement and low-cost.For real-variable networks,including directed networks,weighted networks and delayed networks,many valuable results have been obtained.However,for complex-variable networks,especially for complex-variable networks with distributed time delays,there are few results.On the other hand,distributed time delay is a generation of constant delay and time-varying delay,and can describe the real systems better.Thus,the synchronization and sample control of complex-variable networks with distributed time delays deserves further studies.The main contents of this thesis are as follows:In Chapter 1,we introduce the current research states of complex networks,delayed networks and sample control.Further,we present the main contents.In Chapter 2,we consider the synchronization of complex-variable networks with distributed time delays.Firstly,we introduce the network model and some preliminaries.Secondly,we gen-eralize the Jensen inequalities from real field to complex field.Thirdly,according to Lyapunov function method and linear matrix inequalities technique,we derive the sufficient conditions for achieving synchronization.Finally,we perform numerical examples to verify the correctness of the derived results.In Chapter 3,we consider the synchronization of complex-variable networks with both time-varying delay and distributed time delays.Firstly,we introduce the network model and some preliminaries.Secondly,we combine sample control with pinning control to design effective con-trollers for large-scale networks.Thirdly,according to Lyapunov function method and linear matrix inequalities technique,we derive the sufficient conditions for achieving synchronization.Finally,we perform numerical examples to verify the correctness of the derived results.In Chapter 4,we conclude this thesis and propose some issues in our future work.