  We give a controllable energy-preserving and an observable
co-energy-preserving de Branges-Rovnyak functional model realization of an
arbitrary given operator Schur function defined on the complex right-half
plane. We work the theory out fully in the right-half plane, without using
results for the disk case, in order to expose the technical details of
continuous-time systems theory. At the end of the article, we make explicit the
connection to the corresponding classical de Branges-Rovnyak realizations for
Schur functions on the complex unit disk.
