De Branges-Rovnyak realizations of operator-valued Schur functions on the complex right half-plane

TL;DR

This paper develops explicit de Branges-Rovnyak functional models for operator-valued Schur functions on the complex right-half plane, emphasizing continuous-time systems theory without relying on disk case results.

Contribution

It provides controllable energy-preserving and observable co-energy-preserving realizations directly in the right-half plane, expanding the theory beyond the classical disk setting.

Findings

Explicit realization formulas for operator-valued Schur functions.

Connection established between right-half plane and disk case models.

Enhanced understanding of continuous-time systems theory in this context.

Abstract

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.