Standard diffusive systems as well-posed linear systems

Abstract

In this paper we show that every diusive system is a well-posed system in the sense of Salamon and Weiss. Furthermore, we characterize several systems theoretic properties of these systems, such as stability, controllability, and observability. Instead of referring to general results on well-posed linear system, we prove these results directly. Hence we hope that this paper will serve as a tutorial to well-posed linear systems.