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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
LAAS - Laboratoire d'analyse et d'architecture des systèmes
Abstract : 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.
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Submitted on : Tuesday, May 22, 2018 - 9:17:16 AM
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  • HAL Id : hal-01796803, version 1

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

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