Well-posedness and regularity of hyperbolic boundary control systems on a one-dimensional spatial domain
Hans Zwart, Yann Le Gorrec, Bernhard Maschke, Javier Villegas (2010)
ESAIM: Control, Optimisation and Calculus of Variations
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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 -semigroup. Furthermore, we show that the corresponding transfer function is regular, , has a limit for going to infinity.