Les inéquations matricielles linéaires: un outil intéressant en théorie des systèmes et du contrôle

  • Benjamin TOSSENS

Student thesis: Master typesMaster in Mathematics

Abstract

Based on the course Linear Matrix Inequalities in Control developped by Carsten Scherer and Siep Weiland, this report presents the linear matrix inequalities with illustrations, their most important properties and various results in which the linear matrix inequalities have a impact. After this essential step about the linear matrix inequalities, we talk about the resolution of convex optimization problems because linear matrix inequalities are convex constraints and we present the ellipsoid method. We see afterwards different notions about the dissipativity a characteristic of the dynamical systems and we examine a few theorems in which linear matrix inesualities give equivalent conditions to the dissipativity. Two kinds of functions are developped here, the supply and storage functions. Then we consider briefly three famous lemmas in control whose the Kalman-Yakubovich-Popov lemma. Finally we discuss the stability of systems in the sense of Lyapunov. We define Lyapunov functions to test conditions of stability in which we can find a kind of linear matrix inequalities. We see two methods to construct these functions and we give a few examples. The linear systems and their results are separalety considered. The contents of this report should be attainable for students in master in mathematics.
Date of Award5 Sep 2011
Original languageFrench
SupervisorJoseph Winkin (Supervisor), Timoteo Carletti (Jury), Jean-Jacques Strodiot (Jury) & Anne Lemaitre (Jury)

Cite this

Les inéquations matricielles linéaires: un outil intéressant en théorie des systèmes et du contrôle
TOSSENS, B. (Author). 5 Sep 2011

Student thesis: Master typesMaster in Mathematics