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Polynomial Approximation of Quasipolynomials Based on Digital Filter Design Principles

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Book cover Automation Control Theory Perspectives in Intelligent Systems (CSOC 2016)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 466))

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Abstract

This contribution is aimed at a possible procedure approximating quasipolynomials by polynomials. Quasipolynomials appear in linear time-delay systems description as a natural consequence of the use of the Laplace transform. Due to their infinite root spectra, control system analysis and synthesis based on such quasipolynomial models are usually mathematically heavy. In the light of this fact, there is a natural research endeavor to design a sufficiently accurate yet simple engineeringly acceptable method that approximates them by polynomials preserving basic spectral information. In this paper, such a procedure is presented based on some ideas of discrete-time (digital) filters designing without excessive math. Namely, the particular quasipolynomial is subjected to iterative discretization by means of the bilinear transformation first; consequently, linear and quadratic interpolations are applied to obtain integer powers of the approximating polynomial. Since dominant roots play a decisive role in the spectrum, interpolations are made in their very neighborhood. A simulation example proofs the algorithm efficiency.

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Acknowledgments

The work was performed with the financial support by the Ministry of Education, Youth and Sports of the Czech Republic within the National Sustainability Programme project No. LO1303 (MSMT-7778/2014) and also by the European Regional Development Fund under the project CEBIA-Tech No. CZ.1.05/2.1.00/03.0089.

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Authors and Affiliations

  1. Faculty of Applied Informatics, Tomas Bata University in Zlín, Zlín, Czech Republic

    Libor Pekař & Pavel Navrátil

Authors
  1. Libor Pekař
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  2. Pavel Navrátil
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Corresponding author

Correspondence to Libor Pekař .

Editor information

Editors and Affiliations

  1. Faculty of Applied Informatics, Tomas Bata University in Zlín, Zlín, Czech Republic

    Radek Silhavy

  2. Faculty of Applied Informatics, Tomas Bata University in Zlín, Zlín, Czech Republic

    Roman Senkerik

  3. Faculty of Applied Informatics, Tomas Bata University in Zlín, Zlín, Czech Republic

    Zuzana Kominkova Oplatkova

  4. Faculty of Applied Informatics, Tomas Bata University in Zlín, Zlín, Czech Republic

    Petr Silhavy

  5. Faculty of Applied Informatics, Tomas Bata University in Zlín, Zlín, Czech Republic

    Zdenka Prokopova

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Pekař, L., Navrátil, P. (2016). Polynomial Approximation of Quasipolynomials Based on Digital Filter Design Principles. In: Silhavy, R., Senkerik, R., Oplatkova, Z.K., Silhavy, P., Prokopova, Z. (eds) Automation Control Theory Perspectives in Intelligent Systems. CSOC 2016. Advances in Intelligent Systems and Computing, vol 466. Springer, Cham. https://doi.org/10.1007/978-3-319-33389-2_3

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  • DOI: https://doi.org/10.1007/978-3-319-33389-2_3

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-33387-8

  • Online ISBN: 978-3-319-33389-2

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