Analysis And Control Of Global Property And Consensus For A Class Of Nonlinear Network System

The research of complexity and complex system is one of key research topics in the modern science. The complex dynamical network is an important approach to describe and analyze the complex system. It comprises of correlated basic units with certain characteristics and functions. The research on the nonlinear dynamical network system has become one of the popular research areas in the control science field. The pendulum-like system is a typical nonlinear system, and its forward path is the linear time invariant system while its feedback channel is the sector nonlinear perturbation which is periodic. In addition, the investigation of the complex dynamical network with pendulum-like systems also possesses theoretical and practical significance because pendulum-like systems are widely applied in various fields of engineering.This dissertation studies the Lagrange stability, gradient-like property, absolute stability and consensus of a class of discrete complex dynamic network system whose node is the discrete pendulum-like system. With multi-interconnection structure, the methods of controller design to ensure the presence of these properties are proposed. Details are as follows:The research of Lagrange stability and gradient-like property for the network system is concerned. The network system is composed of the pendulum-like systems, and the interconnecting mode includes interconnection between states and interconnection between nonlinear terms. Based on the frequency domain criterion presented by Leonov and the KYP lemma, the time domain criteria for the Lagrange stability and gradient-like property of the network system are derived. By using the projection lemma and Schur complement lemma, an analysis method of the gradient-like property based on a linear matrix inequality(LMI) is given. Besides, the state feedback controllers are designed on the basis of LMI criteria to guarantee the Lagrange stability and gradient-like behavior of the closed-loop network system.The absolute stability and consensus of the network system whose node is another type of discrete pendulum-like system are also discussed. Based on the Lyapunov stability theory, the time domain criterion of absolute stability for the discrete pendulum-like system is presented. S-procedure is adopted to reduce the conservation of the criterion, and KYP lemma is used to obtain the frequency domain criterion. The time and frequency domain criterion are given by adding the output interconnection on the basis of state interconnection and nonlinear interconnection. By applying a linear transformation matrix, the problem of consensus is converted to the partial stability problem of a corresponding system. Based on the criteria obtained, the state feedback controller and the static output feedback controller which make the closed-loop system consensus are designed. The parameters of the controllers can be obtained through a series of LMIs.