Geodesic
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

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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.

DOI : 10.1051/cocv/2009036
Classification : 93C20, 35L40, 35F15, 37Kxx
Keywords: infinite-dimensional systems, hyperbolic boundary control systems, C0-semigroup, well-posedness, regularity 
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     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},
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     year = {2010},
     doi = {10.1051/cocv/2009036},
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     zbl = {1202.93064},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2009036/}
}
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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

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