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

Published online by Cambridge University Press:  25 August 2009

Hans Zwart ,
Yann Le Gorrec ,
Bernhard Maschke  and
Javier Villegas
Hans Zwart
Affiliation:
Department of Applied Mathematics, University of Twente, 7500 AE Enschede, The Netherlands. h.j.zwart@math.utwente.nl
Yann Le Gorrec
Affiliation:
FEMTO-ST AS2M, 24 rue Alain Savary, 25000 Besançon, France. Yann.Le.Gorrec@ens2m.fr
Bernhard Maschke
Affiliation:
LAGEP, CNRS UMR 5007, CPE Lyon – Bâtiment 308 G, Université Lyon-1, Université de Lyon, 43 bd. du 11 Novembre 1918, 69622 Villeurbanne Cedex, France. maschke@lagep.univ-lyon1.fr
Javier Villegas
Affiliation:
AVL Powertrain UK, Langdale House, Sable Way, Southfields Business Park, Basildon, SS15 6SR, UK. Javier.Villegas@avl.com
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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 C 0-semigroup. Furthermore, we show that the corresponding transfer function is regular, i.e., has a limit for s going to infinity.

Keywords

Infinite-dimensional systemshyperbolic boundary control systemsC 0-semigroupwell-posednessregularity
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 16 , Issue 4 , October 2010 , pp. 1077 - 1093
Copyright
© EDP Sciences, SMAI, 2009

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