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Output Feedback in Descriptor Systems

  • Conference paper
Book cover Linear Algebra for Control Theory

Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 62))

Abstract

A summary is given of conditions under which a descriptor, or generalized state-space, system can be regularized by output feedback. Theorems are presented showing that under these conditions proportional and derivative output feedback controls can be constructed such that the closed loop system is regular and has index at most one. This property ensures the solvability of the resulting system of dynamic-algebraic equations. A canonical form is given that allows the system properties as well as the feedback to be determined. The construction procedures used to establish the theory are based only on orthogonal matrix decompositions and can therefore be implemented in a numerically stable way. A computational algorithm for improving the ‘conditioning’ of the regularized closed loop system is described.

Partial support received from British Council/DAAD ARC Project No. 127.

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Author information

Authors and Affiliations

  1. Fachbereich Mathematik und Informatik, Universität Bremen, Bibliotheksstrasse, D-2800, Bremen 33, Germany

    Angelika Bunse-Gerstner

  2. Diskrete Strukturen in der Mathematik, Universität Bielefeld, Germany

    Angelika Bunse-Gerstner

  3. FSP Mathematisierung, Universität Bielefeld, Germany

    Angelika Bunse-Gerstner & Volker Mehrmann

  4. Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, D-4800, Bielefeld 1, Germany

    Volker Mehrmann

  5. Department of Mathematics, University of Reading, Box 220, Reading, RG6 2AX, UK

    Nancy K. Nichols

Authors
  1. Angelika Bunse-Gerstner
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  2. Volker Mehrmann
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  3. Nancy K. Nichols
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Editor information

Editors and Affiliations

  1. Coordinated Science Laboratory, University of Illinois at Urbana-Champaign, 138 W. Main Street, Urbana, IL, 61801, USA

    Paul Van Dooren

  2. Department of Mathematics, Ohio State University, 100 Mathematics Building, 231 West 18th Avenue, Columbus, OH, 43210-1174, USA

    Bostwick Wyman

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© 1994 Springer-Verlag New York, Inc.

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Bunse-Gerstner, A., Mehrmann, V., Nichols, N.K. (1994). Output Feedback in Descriptor Systems. In: Van Dooren, P., Wyman, B. (eds) Linear Algebra for Control Theory. The IMA Volumes in Mathematics and its Applications, vol 62. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8419-9_4

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  • DOI: https://doi.org/10.1007/978-1-4613-8419-9_4

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4613-8421-2

  • Online ISBN: 978-1-4613-8419-9

  • eBook Packages: Springer Book Archive

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