On the use of the Wirtinger inequalities for time-delay systems

Alexandre Seuret 1 Frédéric Gouaisbaut 2
1 NECS - Networked Controlled Systems
Inria Grenoble - Rhône-Alpes, GIPSA-DA - Département Automatique
2 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande
LAAS - Laboratoire d'analyse et d'architecture des systèmes [Toulouse]
Abstract : The paper addresses the stability problem of linear time delay system. In the literature, the most popular approach to tackle this problem relies on the use of Lyapunov-Krasovskii functionals. Many results have proposed new functionals and techniques for deriving less and less conservative stability conditions. Nevertheless, all these approaches use the same trick, the well-known Jensen's inequality which generally induces some conservatism difficult to overcome. In light of those observations, we propose to reduce the conservatism of Lyapunov-Krasovskii functionals by introducing new classes of integral inequalities called Wirtinger inequalities. This integral type inequality is rstly shown to encompass Jensen's inequality and is then employed to derive new stability conditions. To this end, a slightly modi ed Lyapunov functional is proposed. Several examples illustrate the e ectiveness of our methodology.
Type de document :
Communication dans un congrès
10th IFAC Workshop on Time Delay Systems, Jun 2012, Boston, United States. 6 p., 2012
Liste complète des métadonnées

Littérature citée [18 références]  Voir  Masquer  Télécharger

https://hal.archives-ouvertes.fr/hal-00697498
Contributeur : Alexandre Seuret <>
Soumis le : mardi 15 mai 2012 - 15:18:24
Dernière modification le : mercredi 11 janvier 2017 - 01:02:24
Document(s) archivé(s) le : jeudi 16 août 2012 - 02:41:07

Fichier

WirtingerTDS.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-00697498, version 1

Citation

Alexandre Seuret, Frédéric Gouaisbaut. On the use of the Wirtinger inequalities for time-delay systems. 10th IFAC Workshop on Time Delay Systems, Jun 2012, Boston, United States. 6 p., 2012. 〈hal-00697498〉

Partager

Métriques

Consultations de la notice

797

Téléchargements de fichiers

770