Positive Real Control For Linear Systems Based On Observer

The positive real control problem for the observer-based 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. Then we give the summary of positive realness and its application in stability studies as well as control and system thedry, the main results of this research.In the second part, the observer-based positive real control problem for a class of linear neutral delay systems is considered. The positive realness condition of the nominal systems is provided. Then we give a sufficient condition for the existence of the observer-based controller in the form of linear matrix inequalities. Numerical example is given to demonstrate the applicability of the proposed approach.In the third part, the problem of positive real control for a class of linear discrete-time systems with norm-bounded uncertainties is considered. By casting this problem into a class of strict positive real control problems with scaling parameters, uncertainty-independent solutions are then 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 is extended strictly positive realness. Then numerical example is given to demonstrate the validity of the approach.