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QPmR - Quasi-Polynomial Root-Finder: Algorithm Update and Examples

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Book cover Delay Systems

Part of the book series: Advances in Delays and Dynamics ((ADVSDD,volume 1))

Abstract

An updated QPmR algorithm implementation for computation and analysis of the spectrum of quasi-polynomials is presented. The objective is to compute all the zeros of a quasi-polynomial located in a given region of the complex plane. The root-finding task is based on mapping the quasi-polynomial in the complex plane. Consequently, utilizing spectrum distribution diagram of the quasi-polynomial, the asymptotic exponentials of the retarded chains are determined. If the quasi-polynomial is of neutral type, the spectrum of associated exponential polynomial is assessed, supplemented by determining the safe upper bound of its spectrum. Next to the outline of the computational tools involved in QPmR, its Matlab implementation is presented. Finally, the algorithm is demonstrated by three examples.

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Authors and Affiliations

  1. Department of Instrumentation and Control Engineering, Faculty of Mechanical Engineering, Czech Technical University in Prague, Technická 4, 166 07, Praha 6, Czech Republic

    Tomáš Vyhlídal & Pavel Zítek

Authors
  1. Tomáš Vyhlídal
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  2. Pavel Zítek
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Corresponding author

Correspondence to Tomáš Vyhlídal .

Editor information

Editors and Affiliations

  1. Dept. of Instrumentation & Control Eng. Faculty of Mechanical Engineering, Czech Technical University, Prague, Czech Republic

    Tomáš Vyhlídal

  2. Institut de Recherche en Communications et Cybernétique de Nantes, Nantes Cedex 3, France

    Jean-François Lafay

  3. Department of Mechanical and Industrial Engineering, Northeastern University, Boston, Massachusetts, USA

    Rifat Sipahi

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Vyhlídal, T., Zítek, P. (2014). QPmR - Quasi-Polynomial Root-Finder: Algorithm Update and Examples. In: Vyhlídal, T., Lafay, JF., Sipahi, R. (eds) Delay Systems. Advances in Delays and Dynamics, vol 1. Springer, Cham. https://doi.org/10.1007/978-3-319-01695-5_22

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  • DOI: https://doi.org/10.1007/978-3-319-01695-5_22

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-01694-8

  • Online ISBN: 978-3-319-01695-5

  • eBook Packages: EngineeringEngineering (R0)

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