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Polynomial Approximation of Quasipolynomials Based on Digital Filter Design Principles

  • Libor PekařEmail author
  • Pavel Navrátil
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 466)

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.

Keywords

Approximation Bilinear transformation Digital filter MATLAB Polynomials Pre-warping Quasipolynomials 

Notes

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. 1.Faculty of Applied InformaticsTomas Bata University in ZlínZlínCzech Republic

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