Stability analysis of a system coupled to a heat equation. - LAAS - Laboratoire d'Analyse et d'Architecture des Systèmes Access content directly
Journal Articles Automatica Year : 2019

Stability analysis of a system coupled to a heat equation.


As a first approach to the study of systems coupling finite and infinite dimensional natures, this article addresses the stability of a system of ordinary differential equations coupled with a classic heat equation using a Lyapunov functional technique. Inspired from recent developments in the area of time delay systems, a new methodology to study the stability of such a class of distributed parameter systems is presented here. The idea is to use a polynomial approximation of the infinite dimensional state of the heat equation in order to build an enriched energy functional. A well known efficient integral inequality (Bessel inequality) will allow to obtain stability conditions expressed in terms of linear matrix inequalities. We will eventually test our approach on academic examples in order to illustrate the efficiency of our theoretical results.
Fichier principal
Vignette du fichier
BSG-VF-HAL.pdf (2.33 Mo) Télécharger le fichier
Origin Files produced by the author(s)

Dates and versions

hal-01566455 , version 1 (21-07-2017)
hal-01566455 , version 2 (10-12-2018)



Lucie Baudouin, Alexandre Seuret, Frédéric Gouaisbaut. Stability analysis of a system coupled to a heat equation.. Automatica, 2019, 99, pp.195-202. ⟨10.1016/j.automatica.2018.10.021⟩. ⟨hal-01566455v2⟩
461 View
1098 Download



Gmail Mastodon Facebook X LinkedIn More