Polynomial Parameter Dependent Robust Stability Analysis And Robust Stabilization For Research

There always is some unknown but inevitable factors exit in the actual system. When analyze and deign, they will arouse the disparities between the model and the real object. In order to make the system preserve its characters, full consideration must be paid to the uncertainties and the perturbations in the design. On the practicing background, the robust theory has produced, and gradually developed into an important aspect in control theory and the engineering area. There are two facets in robust theory: fist is the stability robustness of the system, the other is the synthesis of robustness.The front of the paper introduced the base of the research—stability theory of Lyapunov and LMI which used as an important tool in the analysis. The third chapter gave the sufficient conditions of the parameter polynomial-dependent linear systems, the robust asymptotically stability of the system is transformed into feasibility test of a pair of linear matrix inequalities (LMIs). The result presented in this article is less conservative comparing with the previous result that is based on quadratic Lyapunov function. A numerical example shows the validity of the result.The fourth chapter discussed the robust performance of the uncertain system. In this part, we transformed the question to the solution of LMIs, and the result was examined by the LMI toolbox of Matlab.This paper also presented the method of gain-scheduled robust controller design on the basis of LMI, and gave the sufficient conditions to guarantee the existence of the robust controllers.The last part concluded the work of the paper, analyzed the situation of research to uncertain system with the progress of this area, and pointed out that what we can do in the future in this direction.