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Stability analysis of an ordinary differential equation interconnected with the reaction-diffusion equation

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 : This paper deals with the analysis reaction diffusion equation, which can be found in many applications such as in pharmaceutic or chemistry fields. The particularity of the present paper is to study the interconnection of this class of infinite-dimensional systems to a finite-dimensional systems. In this situation, stability is not straightforward to assess any more and one needs to look for dedicated tools to provide accurate numerical tests. Here, the objective is to provide a Lyapunov analysis leading to efficient and scalable stability criteria. This is made possible thanks to the Legendre orthogonal basis which allows building accurate Lyapunov functionals. Indeed this functional is expressed thanks to the state of the finite-dimensional system, the first Fourier-Legendre coefficients and the remainder of the Fourier-Legendre expansion of the infinite-dimensional state. Using this representation, efficient formulation of the Bessel and Wirtinger inequalities are provided leading to sufficient stability conditions expressed in terms of linear matrix inequalities. Numerical examples finally illustrate the accuracy and the potential of the stability result.
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https://hal.laas.fr/hal-03150194
Contributor : Alexandre Seuret Connect in order to contact the contributor
Submitted on : Tuesday, February 23, 2021 - 3:46:27 PM
Last modification on : Monday, July 4, 2022 - 8:37:17 AM
Long-term archiving on: : Monday, May 24, 2021 - 8:35:56 PM

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  • HAL Id : hal-03150194, version 1

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Mathieu Bajodek, Alexandre Seuret, Frédéric Gouaisbaut. Stability analysis of an ordinary differential equation interconnected with the reaction-diffusion equation. 2021. ⟨hal-03150194⟩

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