A conservative de Branges-Rovnyak functional model for operator Schur functions on C+

We present a solution of the operator-valued Schur-function realizationproblem on the right-half plane by developing the corresponding deBranges-Rovnyak canonical conservative simple functional model. This modelcorresponds to the closely connected unitary model in the disk setting, but wework the theory out directly in the right-half plane, which allows us toexhibit structure which is absent in the disk case. A main feature of the studyis that the connecting operator is unbounded, and so we need to make use of thetheory of well-posed continuous-time systems. In order to strengthen theclassical uniqueness result (which states uniqueness up to unitary similarity),we introduce non-invertible intertwinements of system nodes.