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

Zwart, Hans; Le Gorrec, Yann; Maschke, Bernhard; Villegas, Javier

ESAIM: Control, Optimisation and Calculus of Variations, Tome 16 (2010) no. 4, pp. 1077-1093.

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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