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Computation of the \(\mathcal {L}_{\infty }\)-norm of Finite-Dimensional Linear Systems

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Maple in Mathematics Education and Research (MC 2020)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1414))

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Abstract

In this paper, we study the problem of computing the \(\mathcal {L}_{\infty }\)-norm of finite-dimensional linear time-invariant systems. This problem is first reduced to the computation of the maximal x-projection of the real solutions \((x, \, y)\) of a bivariate polynomial system \({\varSigma = \,}\{P,\frac{\partial P}{\partial y}\}\), with \(P\, \in \mathbb {Z}[x,y]\). Then, we use standard computer algebra methods to solve the problem. In this paper, we alternatively study a method based on rational univariate representations, a method based on root separation, and finally a method first based on the sign variation of the leading coefficients of the signed subresultant sequence and then based on the identification of an isolating interval for the maximal x-projection of the real solutions of \(\varSigma \).

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Notes

  1. 1.

    The experiments were conducted on Intel(R) Core(TM) i7-7500U CPU @ 2.70 GHz 2.90 GHz, Installed RAM 8.00 GB under a Windows platform.

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Authors and Affiliations

  1. Inria Lille Europe, IMJ – PRG, Sorbonne University, Paris, France

    Yacine Bouzidi

  2. Inria Paris, Ouragan Project, IMJ – PRG, Sorbonne University, Paris, France

    Alban Quadrat, Fabrice Rouillier & Grace Younes

Authors
  1. Yacine Bouzidi
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  2. Alban Quadrat
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  3. Fabrice Rouillier
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  4. Grace Younes
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Corresponding author

Correspondence to Grace Younes .

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Editors and Affiliations

  1. Western University, London, ON, Canada

    Robert M. Corless

  2. Maplesoft, Waterloo, ON, Canada

    Jürgen Gerhard

  3. Wilfrid Laurier University, Waterloo, ON, Canada

    Ilias S. Kotsireas

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Bouzidi, Y., Quadrat, A., Rouillier, F., Younes, G. (2021). Computation of the \(\mathcal {L}_{\infty }\)-norm of Finite-Dimensional Linear Systems. In: Corless, R.M., Gerhard, J., Kotsireas, I.S. (eds) Maple in Mathematics Education and Research. MC 2020. Communications in Computer and Information Science, vol 1414. Springer, Cham. https://doi.org/10.1007/978-3-030-81698-8_9

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  • DOI: https://doi.org/10.1007/978-3-030-81698-8_9

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  • Online ISBN: 978-3-030-81698-8

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