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.

Classification: 93C20, 35L40, 35F15, 37Kxx

Keywords: 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}, publisher = {EDP-Sciences}, volume = {16}, number = {4}, year = {2010}, pages = {1077-1093}, doi = {10.1051/cocv/2009036}, zbl = {1202.93064}, mrnumber = {2744163}, language = {en}, url = {http://www.numdam.org/item/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, Volume 16 (2010) no. 4, pp. 1077-1093. doi : 10.1051/cocv/2009036. http://www.numdam.org/item/COCV_2010__16_4_1077_0/

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