Lyapunov stability of a coupled ordinary differential system and a string equation with polytopic uncertainties

Matthieu Barreau (1) , Alexandre Seuret (1) , Frédéric Gouaisbaut (1)

1 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande

This chapter deals about the robust stability analysis of a coupled system made up of an uncertain ordinary differential system and a string equation. The main result states the robust exponential stability of this interconnected system subject to polytopic uncertainties. The Lyapunov theory transforms the stability analysis into the resolution of a set of linear matrix inequalities. They are obtained using projections of the infinite dimensional state onto the orthogonal basis of Legendre poly-nomials. The special structure of these inequalities is used to derive robust stability results. An example synthesizes the two main contributions of this chapter: an extended stability result and a robustness analysis. The example shows the efficiency of the proposed method.

Domaines: Optimisation et contrôle [math.OC]; Equations aux dérivées partielles [math.AP]

Matthieu Barreau, Alexandre Seuret, Frédéric Gouaisbaut. Lyapunov stability of a coupled ordinary differential system and a string equation with polytopic uncertainties. 2017. ⟨hal-01796803⟩