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On the Use of Functional Models in Model Reduction

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Perspectives in Mathematical System Theory, Control, and Signal Processing

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 398))

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Abstract

It has been known for some time that the Sylvester equation plays a significant role in interpolation, feedback control, observer theory and model reduction problems. In this paper, in place of state space techniques, we use polynomial models to replace the standard Sylvester equation by a polynomial version. The polynomial Sylvester equation is closely related to a Bezout equation. We use this functional setting to unify various model reduction techniques.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Ben-Gurion University of the Negev, Beer Sheva, Israel

    Paul A. Fuhrmann

  2. Institut für Mathematik, Universität Würzburg, Würzburg, Germany

    Uwe Helmke

Authors
  1. Paul A. Fuhrmann
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  2. Uwe Helmke
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Editor information

Editors and Affiliations

  1. ESAT, K.U.Leuven, Kasteelpark Arenberg 10, 3001, Leuven, Belgium

    Jan C. Willems

  2. Department of Information Physics and Computing, Graduate School of Information Science and Technology, The University of Tokyo, 7-3-1, Hongo, Bunkyo-ku, 113-8656, Tokyo, Japan

    Shinji Hara

  3. Control Systems Theory Group, Department of Applied Mathematics and Physics , Graduate School of Informatics, Kyoto University, Yoshida-honmachi, 606-8501, Kyoto, Japan

    Yoshito Ohta

  4. Dept. Applied Analysis & Complex Dynamic Systems, Kyoto University, 606-8501, Kyoto, Japan

    Hisaya Fujioka

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Fuhrmann, P.A., Helmke, U. (2010). On the Use of Functional Models in Model Reduction. In: Willems, J.C., Hara, S., Ohta, Y., Fujioka, H. (eds) Perspectives in Mathematical System Theory, Control, and Signal Processing. Lecture Notes in Control and Information Sciences, vol 398. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-93918-4_16

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  • DOI: https://doi.org/10.1007/978-3-540-93918-4_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-93917-7

  • Online ISBN: 978-3-540-93918-4

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