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

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.

Mots clés: Lyapunov functionals; integral inequalities; Heat equation; LMI

Domaines: Automatique / Robotique

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. ⟨hal-01496115v2⟩