Study On Stability And Control For Complex Network

Complex network and complexity have caused a considerable interest in the study of science and engineering in recent years. Nature and society are filled with various networks, such as WWW, Internet, metabolic network, society network, etc. We are living in the world filled with all kinds of networks. With the fast development of modern science and industry, the control systems we are faced becoming more and more complicated, many of them are composed of two different kinds of variable in nature, they are hybird dynamic systems, which are composed of discrete event driven system and continuous variable dynamic system. The dynamic behaviors of the systems will become more complicated and the traditional theory cannot solve this problem. It is necessary to develop a method to study the dynamical behavior of hybrid system and hybrid complex network, which can help to improve the stability, safety and efficiency of the system.In this dissertation, a class of complex dynamic network was stabilized by a hybrid controller. The hybrid complex dynamical network is always more complicated than hybrid systems, because besides the complex caused by hybrid system, the coupling topology add difficulty to the network. Based on Lyapunov function, inequality techniques, the global stability and local stability of such network have been studied, the controller was also given. A model of hybrid complex network with spatio-temporal switches has been established and the stability of such network was studied. Based on a switching Lyapunov function method, some sufficient conditions for the stability of the network under arbitrary switching were derived.For the physical scientists, the terminal object to study the network is to understand how topology affecting the physical process. Synchronization is one of the important phenomena of network. In this dissertation, various type of complex network's synchronization phenomena have been studied, such as the global synchronization of heterogeneous delay complex network, the global synchronization of homogeneous delay complex network, the local synchronization of complex network with coupling delay. Based on Lyapunov function, mathematic inequality, linear matrix inequality technique and impulsive equation theory, some synchronization conditions were derived.For the impulsive complex network and topology changing impulsive complex network, the dissipativity and stability of such complex dynamic network have been studied and the controllers were given.For the hybrid stochastic system, the stochastic robust stability and dissipative control problem have been studied. Such system, including impulsive, markovian jump and time-delay. The conditions that guaranteed such system stochastic robust stable and strictly dissipative was given even if some specified actuator was failed, and the controller was given.For the Internet-based network, a network model with local control, remote control, switching, time-delay was established. The stability and dissipativity of such Internet-based network were studied. Some conditions that under some switching rule or arbitrary switching that can make the network stable or dissipative were given.Finally, a summary has been done for all discussion in the dissertation. The research works in further study are presented.