Finite-time Synchronization And Control Of A Class Of Drive-response Complex Networks

Based on the finite-time stability theory, recurring to LMI toolbox and simulation inMatlab, we will study the finite-time synchronization of general drive-response complexnetworks. Under design a suitable control, by constructing the suitable Lyapunovfunctional and applying appropriate inequality technique, the sufficient conditions aboutfinite-time synchronization of those complex networks could be obtained. Meanwhile, wewill give numerical examples to illustrate the effectiveness and feasibility in the end ofeach chapter.The whole thesis consists of five chapters.Chapter1is introduction, the development of complex networks and current advanceof study on the synchronization control and the application in synchronization of complexnetwork model are given. Meanwhile, the current advance of existing problem at this stageis also introduced briefly, and the program of this dissertation is given too.In the second chapter, we consider the drive-response complex network. Based onfinite-time stability theory, by constructing Lyapunov functional, some sufficient controlcriteria are given for the finite-time synchronization. This chapter has analyzed thesynchronization ability, also has taken into account—the more unknown parameters of thesystem are，the longer in time to achieve finite-time synchronization will be. Hence, theresults of this chapter have more practical application value.In the third chapter, the finite-time impulsive synchronization and finite-timesynchronization via periodically intermittent control for a class of drive-response complexnetworks with time delay are investigated. Based on assuming that the node dynamicsfunction satisfies the global Lipschitz condition, the sufficient conditions for the finite-timeimpulsive synchronization and finite-time synchronization via periodically intermittentcontrol are deserved by constructing proper Lyapunov functions and differential inequalitytechnique.In the fourth chapter, we study the finite-time synchronization via adaptiveintermittent control and feedback intermittent control for a class drive-response complexnetwork. Several sufficient criterions in linear matrix inequality form for the finite-timesynchronization via adaptive intermittent control and feedback intermittent control of thecomplex networks are obtained by virtue of Lyapunov functions and differential inequality.In the fifth chapter, we will summarize the whole work of the thesis and point out thedeveloping directions that needs to be further explored in the future.