Simultaneous Stabilization And Control Study Of Time-delay Systems

Simultaneous stabilization is an important issue in the field of control, it has broad application in real life. But in the actual system, the existence of time-delay often makes the system performance becomes poor, lead to instability of the system, and at the same time, because of some uncertainties in the system, such as some uncertain factors in the process of modeling, and a variety of error and so on, these will affect the performance of the system, therefore, the study of simultaneous stabilization and control of time-delay systems, especially the time-delay systems with uncertainty is of great significance.This thesis, by approach of linear matrix inequality (LMI), Lyapunov-Krasovskii functional and so on, based on Lyapunov stability theory, studies the simultaneous stabilization and simultaneous H? control for time-delay systems and simultaneous H? guaranteed cost control for uncertain nonlinear time-delay systems, the main research content includes the following aspects:1. Study the simultaneous stabilization problem for a class of nonlinear systems with time-delay, by extending the concept of the CLF which is established for ordinary differential systems, this thesis defines the concept of Control Lyapunov-Krasovskii Functional (CL-KF) which is applicable to the time-delay systems, and by the technique of CL-KF, the method of constructing the state feedback stabilization controller is introduced and the effectiveness of this method is verified by a given example, improving the existing research results, and then, the simultaneous stabilization for another class of nonlinear systems is studied by means of output feedback, a sufficient condition for the existence of dynamic output feedback controller and its construction method are given.2. Through state feedback and static output feedback respectively discusses the simultaneous H? control for two classes of time-delay systems. Using Lyapunov-Krasovskii functional as well as the method of LMI, a sufficient condition for the existence of simultaneous H? state feedback controller and its construction method are given, generalizes the achievements of predecessors, and obtain the static feedback gain by solving a collection of LMI's. The given example demonstrates the effectiveness of the proposed method.3. In view of a class of time-delay systems with parameter uncertainty, discusses its simultaneous H? control, using the CL-KF and linear matrix inequality (LMI) approach, a sufficient condition for the existence of simultaneous H? state feedback controller is given, and a universal formula for constructing a continuous controller which simultaneously stabilizes the systems is derived. On this basis, the problem of simultaneous H? guaranteed cost control for another collection of uncertain systems with time-delay is considered, a static output feedback controller is designed by using LMI method, so as to make the closed-loop systems quadratic stability simultaneously and satisfy H? performance requirements and possess guaranteed cost.