Well-posedness andregularity of hyperbolic boundary control systems on a one-dimensional spatial domain.

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.
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Submitted on : Thursday, July 26, 2012 - 3:30:31 PM
Last modification on : Thursday, February 14, 2019 - 2:28:08 PM

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Hans Zwart, Yann Le Gorrec, Bernhard Maschke, Javier Villegas. Well-posedness andregularity of hyperbolic boundary control systems on a one-dimensional spatial domain.. ESAIM: Control, Optimisation and Calculus of Variations, EDP Sciences, 2010, 16 (4), pp.1077-1093. ⟨10.1051/cocv/2009036⟩. ⟨hal-00721093⟩

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