Lyapunov stability analysis of a string equation coupled with an ordinary differential system

Matthieu Barreau 1 Alexandre Seuret 1 Frédéric Gouaisbaut 1 Lucie Baudouin 1
1 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande
LAAS - Laboratoire d'analyse et d'architecture des systèmes [Toulouse]
Abstract : This paper considers the stability problem of a linear time invariant system in feedback with a string equation. A new Lyapunov functional candidate is proposed based on the use of augmented states which enriches and encompasses the classical Lyapunov functional proposed in the literature. It results in tractable stability conditions expressed in terms of linear matrix inequalities. This methodology follows from the application of the Bessel inequality together with Legendre polynomials. Numerical examples illustrate the potential of our approach through three scenari: a stable ODE perturbed by the PDE, an unstable open-loop ODE stabilized by the PDE and an unstable closed-loop ODE stabilized by the PDE.
Type de document :
Article dans une revue
IEEE Transactions on Automatic Control, Institute of Electrical and Electronics Engineers, 2018, 〈10.1109/TAC.2018.2802495〉
Liste complète des métadonnées

Littérature citée [24 références]  Voir  Masquer  Télécharger

https://hal.laas.fr/hal-01548256
Contributeur : Matthieu Barreau <>
Soumis le : mercredi 22 novembre 2017 - 15:21:15
Dernière modification le : lundi 16 avril 2018 - 09:04:01

Fichiers

2017_String_2.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

Citation

Matthieu Barreau, Alexandre Seuret, Frédéric Gouaisbaut, Lucie Baudouin. Lyapunov stability analysis of a string equation coupled with an ordinary differential system. IEEE Transactions on Automatic Control, Institute of Electrical and Electronics Engineers, 2018, 〈10.1109/TAC.2018.2802495〉. 〈hal-01548256v3〉

Partager

Métriques

Consultations de la notice

48

Téléchargements de fichiers

9