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

93C20
35L40
35F15
37Kxx

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10.1051/cocv/2009036

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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.",

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AU - Le Gorrec, Yann

AU - Maschke, Bernard

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.

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KW - 35L40

KW - 35F15

KW - 37Kxx

U2 - 10.1051/cocv/2009036

DO - 10.1051/cocv/2009036

M3 - Article

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SP - 1077

EP - 1093

JO - ESAIM: Control, Optimization and Calculus of Variations

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

Abstract

Keywords

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