Phd defense : Hao Lu (laboratoire Ampère)

Date de publication : Sep 26, 2013 12:36:50 PM

Auteur : Hao Lu (Laboratoire Ampère)

Lieu : Amphithéâtre Emilie du Châtelet, Bibliothèque Marie Curie (Médiathèque), INSA de Lyon

Date : 1 octobre 2013, 10H

Titre : Approximation and applications of distributed delay

Résumé : A distributed delay is a linear input-output operator with kernel having a finite support, and appears in many control problems. We investigate in this work the distributed delay and its applications. After an introduction on the definition and on the properties of the distributed delay, the numerical implementation problem of distributed delays is analyzed and a general method for its approximation is given. Then we will focus on four applications where distributed delay appears. The first application is concerned with stable inversion and model matching. A new class of stable inversion (resp. model matching) problem for finite dimensional linear time-invariant systems is defined. Such a problem is an approximation of the exact inversion (resp. model matching) problem, where exact inversion or model matching is reached after a finite time, which is a parameter of the problem. The second application we address concerns stabilization and finite spectrum assignment for a class of infinite dimensional systems. The last application we will focus on is related to the observer synthesis for estimation or output control in linear finite dimensional systems. A closed-loop memoryless observer by input injection is introduced. Asymptotic convergence as well as finite time convergence of the estimation are characterized by output injection and input information via a distributed delay. Finally, we will be interested with the introduction of a new class for approximation of distributed parameter systems. Working with the graph topology, we show that under some weak assumptions, such an approximation can be realized using distributed delay.

Mots-clés : Distributed delay, approximation, linear systems, inversion, model matching, time-delay systems, observer design, distributed parameter systems.

Jury :

Jean Jacques LOISEAU (Rapporteur)

Sabine MONDIÉ (Rapporteur)

Catherine BONNET (Examinateur)

Alexandre SEURET (Examinateur)

Michael DI LORETO (Co-directeur de thèse)

Eric BIDEAUX (Directeur de thèse)