# 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

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topZwart, 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 -

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