Properties of the realization of inner functions

Birgit Jacob, Hans Zwart

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    Abstract

    In this paper we investigate state-space realizations of inner functions. We derive necessary and sufficient, conditions on basis of the inner function to have a exactly controllable and exactly observable realization such that the associated C0-semigroup is exponentially stable. Furthermore. we give necessary and sufficient conditions on the inner function such that the C0-semigroup is a group. Combining these results, the C0-semigroup is an exponentially stable C0- group if and only if the inner function is the product of a constant of modulus one and a Blaschke product for which the zeros satisfy the Carleson-Newman condition and the zeros lie in a vertical strip bounded away from the imaginary axis.

    Original languageEnglish
    Title of host publicationEuropean Control Conference, ECC 1999 - Conference Proceedings
    PublisherIEEE
    Pages3411-3414
    Number of pages4
    ISBN (Electronic)9783952417355
    Publication statusPublished - 24 Mar 2015
    Event1999 European Control Conference, ECC 1999 - Karlsruhe, Germany
    Duration: 31 Aug 19993 Sep 1999

    Conference

    Conference1999 European Control Conference, ECC 1999
    Abbreviated titleECC
    CountryGermany
    CityKarlsruhe
    Period31/08/993/09/99

    Keywords

    • exactly controllable and exactly observable realization
    • exponential stability
    • inner function
    • Realization theory

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