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

Joseph A. Ball, Mikael Kurula, Olof J. Staffans, Heiko J. Zwart

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    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.
    Original languageUndefined
    Pages (from-to)723-792
    Number of pages70
    JournalComplex analysis and operator theory
    Volume9
    Issue number4
    DOIs
    Publication statusPublished - Apr 2015

    Keywords

    • EWI-26574
    • De Branges–Rovnyak space
    • Functional model
    • Right half-plane
    • Continuous time
    • Reproducing kernel
    • METIS-315102
    • IR-98688
    • Schur function

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