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Spectral properties of pseudo-resolvents under structured perturbations

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Abstract

The changes in the spectrum caused by structured perturbations of pseudo-resolvents and operators on Banach spaces are considered. In particular, if a point is in the resolvent set of an operator, necessary and sufficient conditions for it to remain in the resolvent set under structured perturbations are given. The structured perturbations of an operator are specified by an operator node that has three generating operators and a characteristic function together with an admissible feedback operator. In addition, the robustness of stability under structured perturbations is analyzed. The results are applied to boundary control systems and impedance passive systems.

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Authors and Affiliations

  1. Department of Mathematics and Computing Science, University of Groningen, 9700 AV, Groningen, The Netherlands

    Ruth F. Curtain

  2. Department of Mathematics, University of Paderborn, Warburger Str. 100, 33098, Paderborn, Germany

    Birgit Jacob

Authors
  1. Ruth F. Curtain
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  2. Birgit Jacob
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Correspondence to Birgit Jacob.

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Curtain, R.F., Jacob, B. Spectral properties of pseudo-resolvents under structured perturbations. Math. Control Signals Syst. 21, 21–50 (2009). https://doi.org/10.1007/s00498-008-0035-y

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  • DOI: https://doi.org/10.1007/s00498-008-0035-y

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