Positive Real Control Problem For Linear Systems And Its Related Studies

The positive real control problem for the linear systems is considered in this paper. The main results can be listed as follows:In the first part, we introduce the development of control theory, including linear control theory and nonlinear control theory, and the focus of the research in current control and system theory, such as robust control and positive realness control. Then the main work of this paper is given.In the second part, the observer-based positive real control problem for a class of linear systems with general uncertainties is considered. By casting this problem into a class of strict positive real control problems with scaling parameters, uncertainty-independent solutions are established and expressed in linear matrix inequalities. The problem we addressed is to design observer-based dynamic output-feedback controllers, such that the closed-loop system extended strictly positive realness. Then the numerical example is given to demonstrate the validity of the approach.In the third part, the problem of stability and positive realness of a class of linear neutral delay systems is considered. The stability and positive realness of a class of general systems is provided. Then we give a sufficient condition for the systems we focus to research. At last, the numerical example is given to demonstrate the validity of the approach.