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

Hans Zwart, Yann Le Gorrec, Bernhard Maschke, Javier Villegas
2009 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 0
more » ... p, well-posedness. * file:artikel/Dirac/well-posedness 4.tex
doi:10.1051/cocv/2009036 fatcat:bsosgj2uyrb4dnkfcphw5sdp2a