Stability analysis in continuous and discrete time, using the Cayley transform

N.C. Besseling, Heiko J. Zwart

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    Abstract

    For semigroups and for bounded operators we introduce the new notion of Bergman distance. Systems with a finite Bergman distance share the same stability properties, and the Bergman distance is preserved under the Cayley transform. This way, we get stability results in continuous and discrete time. As an example, we show that bounded perturbations lead to pairs of semigroups with finite Bergman distance. This is extended to a class of Desch–Schappacher perturbations.
    Original languageUndefined
    Pages (from-to)487-502
    Number of pages16
    JournalIntegral equations and operator theory
    Volume68
    Issue number4
    DOIs
    Publication statusPublished - 2010

    Keywords

    • EWI-19033
    • MSC-47D60
    • Discrete time
    • Stability
    • $C_0$-semigroups
    • IR-75125
    • Cayley transform
    • Continuous time
    • METIS-275758

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