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Well-posedness and regularity of hyperbolic boundary control systems on a one-dimensional spatial domain
E S A I M: Control, Optimisation and Calculus of Variations
We study 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 C 0 -semigroup. Furthermore, we show that the corresponding transfer function is regular, i.e., has a limit for s going to infinity. keywords: Infinite-dimensional systems, hyperbolic boundary control systems, C 0doi:10.1051/cocv/2009036 fatcat:bsosgj2uyrb4dnkfcphw5sdp2a