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Lyapunov stability analysis of a string equation coupled with an ordinary differential system

Matthieu Barreau 1 Alexandre Seuret 1 Frédéric Gouaisbaut 1 Lucie Baudouin 1 
1 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande
LAAS - Laboratoire d'analyse et d'architecture des systèmes
Abstract : This paper considers the stability problem of a linear time invariant system in feedback with a string equation. A new Lyapunov functional candidate is proposed based on the use of augmented states which enriches and encompasses the classical Lyapunov functional proposed in the literature. It results in tractable stability conditions expressed in terms of linear matrix inequalities. This methodology follows from the application of the Bessel inequality together with Legendre polynomials. Numerical examples illustrate the potential of our approach through three scenari: a stable ODE perturbed by the PDE, an unstable open-loop ODE stabilized by the PDE and an unstable closed-loop ODE stabilized by the PDE.
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Submitted on : Wednesday, February 7, 2018 - 9:14:03 AM
Last modification on : Monday, July 4, 2022 - 8:51:24 AM
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Matthieu Barreau, Alexandre Seuret, Frédéric Gouaisbaut, Lucie Baudouin. Lyapunov stability analysis of a string equation coupled with an ordinary differential system. IEEE Transactions on Automatic Control, Institute of Electrical and Electronics Engineers, 2018, 63 (11), pp.3850 - 3857. ⟨10.1109/TAC.2018.2802495⟩. ⟨hal-01548256v4⟩



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