VERGARA-HERMOSILLA, Gastón; MATIGNON, Denis; TUCSNAK, Marius

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VERGARA-HERMOSILLA, Gastón
Institut de Mathématiques de Bordeaux [IMB]

MATIGNON, Denis
Institut Supérieur de l'Aéronautique et de l'Espace [ISAE-SUPAERO]

TUCSNAK, Marius
Institut de Mathématiques de Bordeaux [IMB]

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We study a PDE based 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.< Leer menos

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Well-posed systems

input-output stability

transfer function

infinite dimensional systems

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

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