Lyapunov stability analysis of a linear system coupled to a heat equation

Lucie Baudouin 1 Alexandre Seuret 1 Frédéric Gouaisbaut 1 Marianne Dattas 1
1 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande
LAAS - Laboratoire d'analyse et d'architecture des systèmes [Toulouse]
Abstract : This paper addresses the stability analysis of a system of ordinary differential equations coupled with a classic heat equation using a Lyapunov approach. Relying on recent developments in the area of time-delay systems, a new method to study the stability of such a class of coupled finite/infinite dimensional systems is presented here. It consists in a Lyapunov analysis of the infinite dimensional state of the system using an energy functional enriched by the mean value of the heat variable. The main technical step relies on the use an efficient Bessel-like integral inequality on Hilbert space leading to tractable conditions expressed in terms of linear matrix inequalities. The results are then illustrated on academic examples and demonstrate the potential of this new approach.
Document type :
Conference papers
IFAC World Congress, Jul 2017, Toulouse, France. 6p., 2017
Liste complète des métadonnées

Cited literature [19 references]  Display  Hide  Download

https://hal.laas.fr/hal-01496115
Contributor : Alexandre Seuret <>
Submitted on : Monday, April 3, 2017 - 10:41:49 AM
Last modification on : Thursday, January 11, 2018 - 6:26:20 AM
Document(s) archivé(s) le : Tuesday, July 4, 2017 - 12:37:28 PM

File

BSG-ifacVF.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-01496115, version 2

Citation

Lucie Baudouin, Alexandre Seuret, Frédéric Gouaisbaut, Marianne Dattas. Lyapunov stability analysis of a linear system coupled to a heat equation. IFAC World Congress, Jul 2017, Toulouse, France. 6p., 2017. 〈hal-01496115v2〉

Share

Metrics

Record views

140

Files downloads

125