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Robustness of polynomial stability with respect to unbounded perturbations

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Original languageEnglish
Pages (from-to)331-337
Number of pages7
JournalSystems and Control Letters
Issue number4
Publication statusPublished - 2013
Publication typeA1 Journal article-refereed


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.

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Field of science, Statistics Finland

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