Well-posedness and Regularity of Hyperbolic Boundary Control Systems on a One-dimensional Spatial Domain

Heiko J. Zwart; Yann Le Gorrec; Bernard Maschke; Javier  Villegas

doi:10.1051/cocv/2009036

Well-posedness and Regularity of Hyperbolic Boundary Control Systems on a One-dimensional Spatial Domain

Heiko J. Zwart, Yann Le Gorrec, Bernard Maschke, Javier Villegas

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Abstract

We study a class of hyperbolic partial differential equations on a one dimensional spatial domain with control and observation at the boundary. Using the idea of feedback we show these systems are well-posed in the sense of Weiss and Salamon if and only if the state operator generates a C0-semigroup. Furthermore, we show that the corresponding transfer function is regular, i.e., has a limit for s going to infinity.

Original language	English
Pages (from-to)	1077-1093
Number of pages	17
Journal	ESAIM: Control, Optimization and Calculus of Variations
Volume	16
Issue number	4
DOIs	https://doi.org/10.1051/cocv/2009036
Publication status	Published - Oct 2010

Keywords

Infinite-dimensional systems
Hyperbolic boundary control systems
C0-semigroup
Well-posedness
Regularity

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10.1051/cocv/2009036

ArticleFinal published version, 338 KBLicence: Taverne

Cite this

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AU - Villegas, Javier

PY - 2010/10

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AB - We study a class of hyperbolic partial differential equations on a one dimensional spatial domain with control and observation at the boundary. Using the idea of feedback we show these systems are well-posed in the sense of Weiss and Salamon if and only if the state operator generates a C0-semigroup. Furthermore, we show that the corresponding transfer function is regular, i.e., has a limit for s going to infinity.

KW - Infinite-dimensional systems

KW - Hyperbolic boundary control systems

KW - C0-semigroup

KW - Well-posedness

KW - Regularity

U2 - 10.1051/cocv/2009036

DO - 10.1051/cocv/2009036

M3 - Article

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EP - 1093

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JF - ESAIM: Control, Optimization and Calculus of Variations

IS - 4

ER -

Well-posedness and Regularity of Hyperbolic Boundary Control Systems on a One-dimensional Spatial Domain

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Keywords

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