Robustness of polynomial stability with respect to unbounded perturbations

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    Abstract

    In this paper we present conditions for the preservation of strong and polynomial stability of a strongly continuous semigroup under unbounded finite rank perturbations of its infinitesimal generator. In addition, we also improve recent perturbation results for bounded finite rank perturbations. The results are illustrated with two examples. In the first one we consider the preservation of stability of a one-dimensional wave equation that has been stabilized polynomially with boundary feedback. In the second example we find conditions for the preservation of polynomial stability of a multiplication semigroup under unbounded rank one perturbations.
    Translated title of the contributionRobustness of polynomial stability with respect to unbounded perturbations
    Original languageEnglish
    Pages (from-to)331-337
    Number of pages7
    JournalSystems and Control Letters
    Volume62
    Issue number4
    DOIs
    Publication statusPublished - 2013
    Publication typeA1 Journal article-refereed

    Publication forum classification

    • Publication forum level 2

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