Well-posedness and regularity of hyperbolic boundary control systems on a one-dimensional spatial domain

Hans Zwart; Yann Le Gorrec; Bernhard Maschke; Javier Villegas

ESAIM: Control, Optimisation and Calculus of Variations (2010)

  • Volume: 16, Issue: 4, page 1077-1093
  • ISSN: 1292-8119

Abstract

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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.

How to cite

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Zwart, Hans, et al. "Well-posedness and regularity of hyperbolic boundary control systems on a one-dimensional spatial domain." ESAIM: Control, Optimisation and Calculus of Variations 16.4 (2010): 1077-1093. <http://eudml.org/doc/250761>.

@article{Zwart2010,
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. },
author = {Zwart, Hans, Le Gorrec, Yann, Maschke, Bernhard, Villegas, Javier},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Infinite-dimensional systems; hyperbolic boundary control systems; C0-semigroup; well-posedness; regularity; infinite-dimensional systems; -semigroup},
language = {eng},
month = {10},
number = {4},
pages = {1077-1093},
publisher = {EDP Sciences},
title = {Well-posedness and regularity of hyperbolic boundary control systems on a one-dimensional spatial domain},
url = {http://eudml.org/doc/250761},
volume = {16},
year = {2010},
}

TY - JOUR
AU - Zwart, Hans
AU - Le Gorrec, Yann
AU - Maschke, Bernhard
AU - Villegas, Javier
TI - Well-posedness and regularity of hyperbolic boundary control systems on a one-dimensional spatial domain
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/10//
PB - EDP Sciences
VL - 16
IS - 4
SP - 1077
EP - 1093
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.
LA - eng
KW - Infinite-dimensional systems; hyperbolic boundary control systems; C0-semigroup; well-posedness; regularity; infinite-dimensional systems; -semigroup
UR - http://eudml.org/doc/250761
ER -

References

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