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.
Mots clés : infinite-dimensional systems, hyperbolic boundary control systems, C0-semigroup, well-posedness, regularity
@article{COCV_2010__16_4_1077_0,
author = {Zwart, Hans and Le Gorrec, Yann and Maschke, Bernhard and Villegas, Javier},
title = {Well-posedness and regularity of hyperbolic boundary control systems on a one-dimensional spatial domain},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {1077--1093},
publisher = {EDP-Sciences},
volume = {16},
number = {4},
year = {2010},
doi = {10.1051/cocv/2009036},
mrnumber = {2744163},
zbl = {1202.93064},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv/2009036/}
}
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 PY - 2010 SP - 1077 EP - 1093 VL - 16 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2009036/ DO - 10.1051/cocv/2009036 LA - en ID - COCV_2010__16_4_1077_0 ER -
%0 Journal Article %A Zwart, Hans %A Le Gorrec, Yann %A Maschke, Bernhard %A Villegas, Javier %T Well-posedness and regularity of hyperbolic boundary control systems on a one-dimensional spatial domain %J ESAIM: Control, Optimisation and Calculus of Variations %D 2010 %P 1077-1093 %V 16 %N 4 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2009036/ %R 10.1051/cocv/2009036 %G en %F COCV_2010__16_4_1077_0
Zwart, Hans; Le Gorrec, Yann; Maschke, Bernhard; Villegas, Javier. Well-posedness and regularity of hyperbolic boundary control systems on a one-dimensional spatial domain. ESAIM: Control, Optimisation and Calculus of Variations, Tome 16 (2010) no. 4, pp. 1077-1093. doi : 10.1051/cocv/2009036. http://www.numdam.org/articles/10.1051/cocv/2009036/
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