Robust Positive Real Analysis And Robust Positive Real Control For A Class Of Uncertainty Systems Based On LMI

The robustness of control systems is a hotspot on the current control theory. By comparison, the research of robust stability is much more than performance robustness. Actual systems not only demand robust stability, but also require robust performance. This dissertation considers a class of parameter uncertainties with the polynomial function form of perturbation parameters, and deals with robust positive realness analysis and control issues for systems with the class of uncertainties.Linear matrix inequality (LMI) is a powerful tool to solve control problems developed in the last few years. Many analysis and synthesis problems of the control systems can be transformed into LMI/LMIs. Based on the method of LMI, the design methods of the robust controller, which meet the given performance requirement to the corresponding system, is put forward considering the robust extended strictly positive realness (ESPR) control problem of the uncertainties with the polynomial function form of perturbation parameters.The major contents in this dissertation are as follows:Firstly, robust ESPR analysis is dealt with for a class of systems with polynomial parameter uncertainties. Based on LMI, a sufficient condition of ESPR is provided, and an estimation method of parameter perturbation domain is also given to keep the ESPR of the system.Secondly, existence criteria and design methods of a robust state feedback positive realness controller are discussed and the estimation approach of the ESPR controller which made the maximum robust positive real domain in closed-loop systems is also given.Finally, considering a class of uncertainties with the output feedback problem, the existence criteria and design methods of a robust output feedback positive realness controller are discussed, and design algorithm of the ESPR controller is proposed to maximize the robust positive real domain of the closed-loop system under the way in the paper. The feasibility of the methods given in the paper is examined by the simulation.