Input-to-state stability for bilinear feedback systems

René Hosfeld; Birgit Jacob; Felix L. Schwenninger; Marius Tucsnak

doi:10.1137/23M155788X

Input-to-state stability for bilinear feedback systems

René Hosfeld^*, Birgit Jacob, Felix L. Schwenninger, Marius Tucsnak

^*Corresponding author for this work

Mathematical Systems Theory

Research output: Contribution to journal › Article › Academic › peer-review

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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 Schrödinger equation, a Navier-Stokes system, and a semilinear wave equation.

Original language	English
Pages (from-to)	1369-1389
Number of pages	21
Journal	SIAM journal on control and optimization
Volume	62
Issue number	3
Early online date	9 May 2024
DOIs	https://doi.org/10.1137/23M155788X
Publication status	Published - 2024

Keywords

2024 OA procedure
bilinear systems
C0-semigroups
feedback systems
input-to-state stability
admissibility

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10.1137/23M155788X

23m155788xFinal published version, 401 KBLicence: Taverne

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title = "Input-to-state stability for bilinear feedback systems",

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{\"o}dinger equation, a Navier-Stokes system, and a semilinear wave equation.",

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author = "Ren{\'e} Hosfeld and Birgit Jacob and Schwenninger, {Felix L.} and Marius Tucsnak",

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AU - Hosfeld, René

AU - Jacob, Birgit

AU - Schwenninger, Felix L.

AU - Tucsnak, Marius

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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 Schrödinger equation, a Navier-Stokes system, and a semilinear wave equation.

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KW - bilinear systems

KW - C0-semigroups

KW - feedback systems

KW - input-to-state stability

KW - admissibility

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Input-to-state stability for bilinear feedback systems

Abstract

Keywords

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