Input-to-state stability for bilinear feedback systems

René Hosfeld; Birgit Jacob; Felix Schwenninger; Marius Tucsnak

doi:10.48550/arXiv.2303.04563

Input-to-state stability for bilinear feedback systems

René Hosfeld, Birgit Jacob, Felix Schwenninger, Marius Tucsnak

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Abstract

Input-to-state stability estimates with respect to small initial conditions and input functions for infinite-dimensional systems with bilinear feedback are shown. We apply the obtained results to controlled versions of a viscous Burger equation with Dirichlet boundary conditions, a Schr\"odinger equation, a Navier--Stokes system and a semilinear wave equation.

Original language	English
Publisher	ArXiv.org
DOIs	https://doi.org/10.48550/arXiv.2303.04563
Publication status	Published - 8 Mar 2023

Keywords

math.AP
math.FA
math.OC
93D06, 93D25, 93C10, 47J35, 35B35

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10.48550/arXiv.2303.04563Licence: Other

PreprintFinal published version, 287 KBLicence: Other

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Input-to-state stability for bilinear feedback systems
Hosfeld, R., Jacob, B., Schwenninger, F. L. & Tucsnak, M., 2024, In: SIAM journal on control and optimization. 62, 3, p. 1369-1389 21 p.
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AB - Input-to-state stability estimates with respect to small initial conditions and input functions for infinite-dimensional systems with bilinear feedback are shown. We apply the obtained results to controlled versions of a viscous Burger equation with Dirichlet boundary conditions, a Schr\"odinger equation, a Navier--Stokes system and a semilinear wave equation.

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Input-to-state stability for bilinear feedback systems

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Research output

Input-to-state stability for bilinear feedback systems

Cite this