WELL-POSEDNESS AND REGULARITY OF HYPERBOLIC BOUNDARY CONTROL SYSTEMS ON A ONE-DIMENSIONAL SPATIAL DOMAIN

摘要

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 Co-semigroup. Furthermore, we show that the corresponding transfer function is regular, i.e., has a limit for s going to infinity.