Introducing Linear Matrix Inequalities in a Control Course

Abstract

The important role that linear matrix inequalities have attained in the last years makes it compulsory to include them in the education of a control engineer. As the development of efficient semidefinite programming algorithms date from the early nineties, there is a lack of teaching experience in this field (at least when it is compared with other well established aspects of control theory). This paper proposes a simple way to introduce linear matrix inequalities in a control course. The main objective of the paper is to show that in the formulation of (robust) control problems as linear matrix inequalities a very reduced number of elementary technical results are required. It is illustrated how to introduce, in a progressive way, these technical results along with motivating examples. All of this is done in such a way that it facilitates the assimilation of this important subject. The presented methodology has been successfully applied for more than four years in a doctoral course on control theory.