Sync Hronization Control Of Complex Dynamical Networks

Generally speaking, complex network is closely linked with people’s life, and has a variety of forms of expression. A complex network is defined for each node that a nonlinear system and connected with complex topology relation between the nodes. For a long time, synchronization is a basic concept in science and technology. Synchronous controlling is a strategy through the system coupling or the applied forcing so that to make two or more dynamic system can share the same dynamic behavior. Synchronization is a problem, you ne ed to study complex networks to be solved. Lur’e system in various fields of a class of nonlinear systems and typical of this type of system is widely used in engineering. The dissertation mainly investigates the synchronization problem of a class of comp lex dynamical networks composed of Lur’e systems and the main contributions are listed as follows:Firstly, the synchronization control problem for dynamical complex networks of coupled by Lur’e system is concerned with. Based on a Lur’e-Postnikov function, feedback control strategy and LMI technology, the global synchronization criteria for complex networks with non-symmetric coupling are established. The control gain matrix can be constructed via the feasible solutions of the LMI in MATLAB. Finally, a numerical example shows the effectiveness of the proposed method.Secondly, the synchronization control problem for Lur’e systems with sector and slope restricted nonlinearities is concerned with. A static error feedback controller based on the Lyapunov stability theory is proposed for asymptotic synchronization. The Lyapunov function candidate is chosen as a quadratic form of the error states and nonlinear functions of the systems. The nonlinearities are expressed as convex combinations of sector and slope bounds by using convex properties of the nonlinear function so that equality constraints are converted into inequality constraints. Then, the feedback gain matrix is derived through a linear matrix inequality(LMI) formulation. Finally, a numerical example s hows the effectiveness of the proposed method.Finally, the synchronization control problem for Lur’e systems that have time- varying delays and sector and slope restricted nonlinearities is concerned with. New delay dependent synchronization criteria are derived via linear matrix inequality(LMI) formulation that can be easily solved by various optimization techniques. Sector bounds and slope bounds are employed to the Lyapunov – Krasovskii functional through convex representation of the nonlinearities so that less conservative synchronization conditions are obtained. Numerical examples show effectiveness of the proposed stability condition.