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Balancing Transformations for Infinite-Dimensional Systems with Nuclear Hankel Operator

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Abstract

We consider balancing and model reduction by balanced truncation for infinite-dimensional linear systems. A functional analytic approach to state space transformations leading to balanced realizations is presented. These transformations can be further used to explicitly construct truncated balanced realizations. The presented approach is applicable to bounded well-posed linear systems with nuclear Hankel operator and finite-dimensional input and output space. Controllability and observability are not required.

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Authors and Affiliations

  1. Fachbereich Mathematik, Universität Hamburg, Bundesstraße 55, 20146, Hamburg, Germany

    Timo Reis

  2. Institut für Mathematik, Technische Universität Ilmenau, Weimarer Straße 25, 98693, Ilmenau, Germany

    Tilman Selig

Authors
  1. Timo Reis
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  2. Tilman Selig
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Correspondence to Timo Reis.

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This work was supported by the Klaus-Tschira-Stiftung.

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Reis, T., Selig, T. Balancing Transformations for Infinite-Dimensional Systems with Nuclear Hankel Operator. Integr. Equ. Oper. Theory 79, 67–105 (2014). https://doi.org/10.1007/s00020-013-2105-x

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  • DOI: https://doi.org/10.1007/s00020-013-2105-x

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