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Model Reduction of Periodic Descriptor Systems Using Balanced Truncation

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Model Reduction for Circuit Simulation

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 74))

Abstract

Linear periodic descriptor systems represent a broad class of time evolutionary processes in micro-electronics and circuit simulation. In this paper, we consider discrete-time linear periodic descriptor systems and study the concepts of periodic reachability and observability Gramians. We also discuss a lifted representation of periodic descriptor systems and propose a balanced truncation model reduction method for such systems.The behaviour of the suggested model reduction technique is illustrated using a numerical example.

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Acknowledgements

This work was supported by the Research Network SyreNe—System Reduction for Nanoscale IC Design funded by the German Federal Ministry of Education and Science (BMBF), grants 03BEPAE1 and 03STPAE3. Responsibility for the contents of this publication rests with the authors.

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Authors and Affiliations

  1. Fakultät für Mathematik, TU Chemnitz, 09107, Chemnitz, Germany

    Peter Benner & Mohammad-Sahadet Hossain

  2. Institut für Mathematik, MA 4-5, TU Berlin, Straße des 17.Juni 136, 10623, Berlin, Germany

    Tatjana Stykel

Authors
  1. Peter Benner
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  2. Mohammad-Sahadet Hossain
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  3. Tatjana Stykel
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Corresponding author

Correspondence to Mohammad-Sahadet Hossain .

Editor information

Editors and Affiliations

  1. Inst. Dynamics of Complex Techn. Systems, Max Planck Institute, Sandtorstrasse 1, Magdeburg, 39106, Germany

    Peter Benner

  2. , Fachbereich Mathematik, Universität Hamburg, Bundesstr. 55, Hamburg, 20146, Germany

    Michael Hinze

  3. , Dept. Mathematics & Comp. Sci., Eindhoven University of Technology, P.O.Box 513, Den Dolech 2, HG 8.02, Eindhoven, 5600 MB, Netherlands

    E. Jan W. ter Maten

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Benner, P., Hossain, MS., Stykel, T. (2011). Model Reduction of Periodic Descriptor Systems Using Balanced Truncation. In: Benner, P., Hinze, M., ter Maten, E. (eds) Model Reduction for Circuit Simulation. Lecture Notes in Electrical Engineering, vol 74. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0089-5_11

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  • DOI: https://doi.org/10.1007/978-94-007-0089-5_11

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  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-007-0088-8

  • Online ISBN: 978-94-007-0089-5

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