Synchronization Analysis For Stochastic Switching Complex Networks Under Feedback Control Or The Delay-partition Approach

Motivated by many systems in science and humanities, complex networkswhich consist of interacting dynamical entities with an interplay between dynam-ical states and interaction patterns have been extensively studied in past decades.Synchronization for complex networks is that the states of many connected n-odes are evolving in synchrony. Du to the increasing complexity of the complexnetwork structure, more and more factors disturb synchronization dynamics. Inmany situations, the switching of complex networks structure is inevitable. To-day, complex networks with switching have been extensively applied in variousfelds such as robot control. Furthermore, synchronization problem for complexnetworks with switching has also attracted increasing attention.In the thesis, synchronization problems for switching complex networks un-der feedback control or the delay-partition approach are studied. Firstly, meansquare exponential synchronization for a class of Markovian switching complexnetworks under feedback control and M-matrix approach is analyzed. Secondly,mean square exponential synchronization for two classes of Markovian switch-ing complex networks under feedback control from synchronization control costviewpoint is investigated. Thirdly, fnite-time global synchronization for a classof Markovian jump complex networks with partially unknown transition ratesunder feedback control is discussed. At last, global synchronization for a classof Markovian switching complex networks with mixed time-varying delays in thedelay-partition approach is proposed. The main contents of the thesis are asfollows:(1) Mean square exponential synchronization for a class of Marko-vian switching complex networks under feedback control and M-matrixapproach. The chapter is concerned with mean square exponential synchro-nization for a class of Markovian switching complex networks (MSCNs) withtime-varying delay and stochastic noise under feedback control and M-matrix approach. Firstly, a class of MSCNs with time-varying delay and stochastic noiseis considered. Secondly, by using M-matrix method and feedback control scheme,several sufcient conditions of mean square exponential synchronization are de-rived. At last, two numerical examples and simulations are given to illustratethe efectiveness of the theoretical results.(2) Mean square exponential synchronization for two classes ofMarkovian switching complex networks under feedback control fromsynchronization control cost viewpoint. The chapter is related to meansquare exponential synchronization for two classes of Markovian switching com-plex networks (MSCNs) under linear negative control scheme from synchroniza-tion control cost viewpoint. Two classes of MSCNs are considered. In order toanalyze synchronization controllability for the two classes of MSCNs from syn-chronization control cost viewpoint, synchronization control cost and synchro-nization controllability are defned, respcetively. By utilizing M-matrix proper-ties, a novel Lyapunov function and the stochastic analysis techniques, sufcientcriteria of mean square synchronization and global synchronization for the twoclasses of MSCNs under feedback control are derived. Three numerical examplesand simulations are given to illustrate the efectiveness of the theoretical results.(3) Finite-time global synchronization for a class of Markovianjump complex networks with partially unknown transition rates un-der feedback control. The chapter presents a framework for fnite-time globalsynchronization of Markovian jump complex networks (MJCNs) with partiallyunknown transition rates, time-delays and stochastic noises. Several criteria forfnite-time global synchronization are given by using the stochastic analysis tech-niques and matrix theory. These criteria provide a feasible approach to designlinear feedback controller and to compute fnite-time of global synchronizationfor the addressed MJCNs. Four numerical examples are given to demonstratethe efectiveness of the theoretical results.(4) Global synchronization for a class of Markovian switching com-plex networks with mixed time-varying delays under the delay-partitionapproach. In the chapter, global synchronization problem for a class of Marko- vian switching complex networks (MSCNs) with mixed time-varying delays underthe delay-partition approach is investigated. A novel delay-partition approach isdeveloped to derive sufcient conditions for a new class of MSCNs with mixedtime-varying delays. The proposed delay-partition approach can make globalsynchronization results have lower conservatism. Two numerical examples areprovided to illustrate the efectiveness of the theoretical results.