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Well-Posedness and input-output stability for a system modelling rigid structures floating in a viscous fluid

Vergara-Hermosilla, Gastón and Matignon, Denis and Tucsnak, Marius Well-Posedness and input-output stability for a system modelling rigid structures floating in a viscous fluid. (2020) In: The 21st World Congress of The International Federation of Automatic Control (IFAC 2020), 11 July 2020 - 17 July 2020 (Virtual event, Germany).

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Official URL: https://doi.org/10.1016/j.ifacol.2020.12.1311

Abstract

We study a PDE based linearized model for the vertical motion of a solid floating at the free surface of a shallow viscous fluid. The solid is controlled by a vertical force exerted via an actuator. This force is the input of the system, whereas the output is the distance from the solid to the bottom. The first novelty we bring in is that we prove that the governing equations define a well-posed linear system. This is done by considering adequate function spaces and convenient operators between them. Another contribution of this work is establishing that the system is input-output stable. To this aim, we give an explicit form of the transfer function and we show that it lies in the Hardy space H∞ of the right-half plane.

Item Type:Invited Conference
Additional Information:vol. 53 n°2
Audience (conference):International conference proceedings
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Institut Supérieur de l'Aéronautique et de l'Espace - ISAE-SUPAERO (FRANCE)
Other partners > Institut Polytechnique de Bordeaux - IPB (FRANCE)
Other partners > Université de Bordeaux (FRANCE)
Laboratory name:
Funders:
H2020 project, grant No 765579
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Deposited On:27 Apr 2021 09:12

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