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Insight into the stability analysis of the reaction-diffusion equation interconnected with a finite-dimensional system taking support on Legendre orthogonal basis

Mathieu Bajodek 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 : The stability analysis of the reaction-diffusion subject to dynamic boundary conditions is not straightforward. This chapter proposes a linear matrix inequality criterion which ensures the stability of such infinite-dimensional system. By the use of Fourier-Legendre series, the Lyapunov functional is split into an augmented finite-dimensional state including within it the first Fourier-Legendre coefficients and the residual part. A link between this modelling and Padé approximation is briefly highlighted. Then, from Bessel and Wirtinger inequalities applied to the Fourier-Legendre remainder and using its orthogonality properties, a sufficient condition of stability expressed in terms of linear matrix inequalities is obtained. This efficient and scalable stability condition is finally performed on examples.
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Submitted on : Thursday, November 18, 2021 - 3:07:47 PM
Last modification on : Tuesday, August 9, 2022 - 3:50:57 PM
Long-term archiving on: : Saturday, February 19, 2022 - 7:22:38 PM

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Mathieu Bajodek, Alexandre Seuret, Frédéric Gouaisbaut. Insight into the stability analysis of the reaction-diffusion equation interconnected with a finite-dimensional system taking support on Legendre orthogonal basis. Advances in Distributed Parameter Systems, Springer, pp 93-115, 2022, 978-3-030-94765-1. ⟨10.1007/978-3-030-94766-8_5⟩. ⟨hal-03434998⟩

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