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Balanced State Representations with Polynomial Algebra

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Directions in Mathematical Systems Theory and Optimization

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 286))

Abstract

Algorithms are derived that pass directly from the differential equation describing the behavior of a finite-dimensional linear system to a balanced state representation.

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25.7 References

  1. P.A. Fuhrmann, A Polynomial Approach to Linear Algebra, Springer Verlag, 1996.

    Google Scholar 

  2. F.R. Gantmacher, The Theory of Matrices, Volume 1, Chelsea Publishing Co., 1959.

    Google Scholar 

  3. K. Glover, All optimal Hankel-norm approximations of linear multivariable systems: Relations to approximation, International Journal of Control, volume 43, pages 1115–1193, 1984.

    Article  MathSciNet  Google Scholar 

  4. S.Y. Kung, A new identification method and model reduction algorithm via singular value decomposition, 12-th Asilomar Conference on Circuits, Systems and Computation, pages 705–714, 1978.

    Google Scholar 

  5. J.W. Polderman and J.C. Willems, Introduction to Mathematical Systems Theory: A Behavioral Approach, Springer Verlag, 1998.

    Google Scholar 

  6. P. Rapisarda and J.C. Willems, State maps for linear systems, SIAM Journal on Control and Optimization, volume 35, pages 1053–1091, 1997.

    Article  MATH  MathSciNet  Google Scholar 

  7. J. C. Willems and H. L. Trentelman, On quadratic differential forms, SIAM Journal of Control and Optimization, volume 36, pages 1703–1749, 1998.

    Article  MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. ESAT-SISTA, K.U. Leuven, Kasteelpark Arenberg 10, B-3001, Leuven-Heverlee, Belgium

    Jan C. Willems

  2. Dept. Mathematics, Maastricht University, PO.Box 616, 6200 MD, Maastricht, The Netherlands

    Paolo Rapisarda

Authors
  1. Jan C. Willems
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  2. Paolo Rapisarda
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Editor information

Editors and Affiliations

  1. Department of Automatic Control, Lund Institute of Technology, Box 118, SE-221 00, Lund, Sweden

    Anders Rantzer

  2. School of Engineering and Applied Science, Washington University, One Brookings Drive, St. Louis, MO, 63130, USA

    Christopher I. Byrnes

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© 2003 Springer-Verlag Berlin Heidelberg

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Willems, J.C., Rapisarda, P. (2003). Balanced State Representations with Polynomial Algebra. In: Rantzer, A., Byrnes, C.I. (eds) Directions in Mathematical Systems Theory and Optimization. Lecture Notes in Control and Information Sciences, vol 286. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36106-5_25

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  • DOI: https://doi.org/10.1007/3-540-36106-5_25

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00065-5

  • Online ISBN: 978-3-540-36106-0

  • eBook Packages: Springer Book Archive

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