Research On Synchronization And Pinning Control For Complex Networks With Coupling Delays

Complex networks have become a focal research topic and attracted a great deal of attention in various fields in recent years. Many systems in nature can be modeled as complex networks, which are composed of a large number of highly interconnected dynamical units. Such systems include the Internet net; the World Wide Web; the power network; the local network; the brain; the organization; and so on. 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 hybrid dynamic systems. The dynamic behaviors of the systems will become more complicated and the traditional theory can not solve this problem. So 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.Motivated by the above mentioned discussions, we investigate the synchroniza-tion problems and pinning control for the complex networks with different coupling delays, and the main contributions are summarized as follows:1. The synchronization problems for an array of neural networks with hybrid coupling are presented. Compared with previous networks, the models proposed in this paper are more general because it includes neutral-type and component delays. Based on Lyapunov-Krasovskii functional and the Kronecker product technique, some less conservative sufficient conditions for delay-dependent synchronization cri-teria are obtained, which are derived in the form of linear matrix inequalities and can be easily computed.2. The synchronization problems for a general complex networks with constant or variable coupling delay are presented. Sufficient conditions for the synchroniza-tion problems of complex dynamical networks with bounded time-varying coupling delays are given in terms of Linear Matrix Inequalities(LMI). Firstly, based on a use-ful inequality and Kronecker product technique, a new criterion is obtained, which has fewer unknown variables and is a significant improvement in the performance. Secondly, different from previous results, by employing a new method of weight-ing delays, some less conservative delay-dependent synchronization criterions are derived. 3. A general complex networks with multiple coupling delays is proposed. By linearizing complicated system to some time-delayed subsystems, for the first time, some new criterions are given to ensure the robust synchronization for the complex networks with multiple-delays. Moreover, the present results are also applied to the system with single time delay, and the coupling-configuration matrix are not necessarily symmetric. Since the expression based on linear matrix inequality (LMI) is used, the obtained criteria can be easily checked in practice.4. The pinning synchronization problems for complex networks with single delays or multiple time-varying delays are presented. By some transformation, the synchronization problems of the complex networks are transferred equally into the asymptotical stability problem of a group of delay functional differential equations. Firstly, a linear controller is designed to keep the system synchronized, the results can deal with more complicated situations. Furthermore, applying the same theory, an adaptive pinning control scheme is developed to achieve synchronization of this general complex networks, and the number of nodes which need to control can be easily computed.5. The synchronization problems for complex networks are investigated by Takagi-Sugeno (T-S) fuzzy theory. A novel concept named linear approximation method is firstly proposed to solve the synchronization problems for T-S fuzzy com-plex networks. This novel method can linearize the system into some time-delay subsystems, which can effectively simplify the complicated system and then be easy to acquire the synchronization results.