IDEAS home Printed from https://ideas.repec.org/a/plo/pone00/0178950.html
   My bibliography  Save this article

Gridding discretization-based multiple stability switching delay search algorithm: The movement of a human being on a controlled swaying bow

Author

Listed:
  • Libor Pekař
  • Radek Matušů
  • Roman Prokop

Abstract

Delay represents a significant phenomenon in the dynamics of many human-related systems—including biological ones. It has i.a. a decisive impact on system stability, and the study of this influence is often mathematically demanding. This paper presents a computationally simple numerical gridding algorithm for the determination of stability margin delay values in multiple-delay linear systems. The characteristic quasi-polynomial—the roots of which decide about stability—is subjected to iterative discretization by means of pre-warped bilinear transformation. Then, a linear and a quadratic interpolation are applied to obtain the associated characteristic polynomial with integer powers. The roots of the associated characteristic polynomial are closely related to the estimation of roots of the original characteristic quasi-polynomial which agrees with the system′s eigenvalues. Since the stability border is crossed by the leading one, the switching root locus is enhanced using the Regula Falsi interpolation method. Our methodology is implemented on—and verified by—a numerical bio-cybernetic example of the stabilization of a human-being′s movement on a controlled swaying bow. The advantage of the proposed novel algorithm lies in the possibility of the rapid computation of polynomial zeros by means of standard programs for technical computing; in the low level of mathematical knowledge required; and, in the sufficiently high precision of the roots loci estimation. The relationship to the direct search QuasiPolynomial (mapping) Rootfinder algorithm and computational complexity are discussed as well. This algorithm is also applicable for systems with non-commensurate delays.

Suggested Citation

  • Libor Pekař & Radek Matušů & Roman Prokop, 2017. "Gridding discretization-based multiple stability switching delay search algorithm: The movement of a human being on a controlled swaying bow," PLOS ONE, Public Library of Science, vol. 12(6), pages 1-23, June.
  • Handle: RePEc:plo:pone00:0178950
    DOI: 10.1371/journal.pone.0178950
    as

    Download full text from publisher

    File URL: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0178950
    Download Restriction: no

    File URL: https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0178950&type=printable
    Download Restriction: no

    File URL: https://libkey.io/10.1371/journal.pone.0178950?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Michael Wibral & Nicolae Pampu & Viola Priesemann & Felix Siebenhühner & Hannes Seiwert & Michael Lindner & Joseph T Lizier & Raul Vicente, 2013. "Measuring Information-Transfer Delays," PLOS ONE, Public Library of Science, vol. 8(2), pages 1-19, February.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. David L Gibbs & Ilya Shmulevich, 2017. "Solving the influence maximization problem reveals regulatory organization of the yeast cell cycle," PLOS Computational Biology, Public Library of Science, vol. 13(6), pages 1-19, June.
    2. Sourabh Lahiri & Philippe Nghe & Sander J Tans & Martin Luc Rosinberg & David Lacoste, 2017. "Information-theoretic analysis of the directional influence between cellular processes," PLOS ONE, Public Library of Science, vol. 12(11), pages 1-26, November.
    3. Coulibaly, Saliya & Bessin, Florent & Clerc, Marcel G. & Mussot, Arnaud, 2022. "Precursors-driven machine learning prediction of chaotic extreme pulses in Kerr resonators," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    4. Xiaogeng Wan & Lanxi Xu, 2018. "A study for multiscale information transfer measures based on conditional mutual information," PLOS ONE, Public Library of Science, vol. 13(12), pages 1-30, December.
    5. Shinya Ito & Fang-Chin Yeh & Emma Hiolski & Przemyslaw Rydygier & Deborah E Gunning & Pawel Hottowy & Nicholas Timme & Alan M Litke & John M Beggs, 2014. "Large-Scale, High-Resolution Multielectrode-Array Recording Depicts Functional Network Differences of Cortical and Hippocampal Cultures," PLOS ONE, Public Library of Science, vol. 9(8), pages 1-16, August.
    6. Nicholas Timme & Shinya Ito & Maxym Myroshnychenko & Fang-Chin Yeh & Emma Hiolski & Pawel Hottowy & John M Beggs, 2014. "Multiplex Networks of Cortical and Hippocampal Neurons Revealed at Different Timescales," PLOS ONE, Public Library of Science, vol. 9(12), pages 1-43, December.
    7. Leonidas Sandoval Junior & Asher Mullokandov & Dror Y. Kenett, 2015. "Dependency Relations among International Stock Market Indices," JRFM, MDPI, vol. 8(2), pages 1-39, May.
    8. Daniel Toker & Friedrich T Sommer, 2019. "Information integration in large brain networks," PLOS Computational Biology, Public Library of Science, vol. 15(2), pages 1-26, February.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:plo:pone00:0178950. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: plosone (email available below). General contact details of provider: https://journals.plos.org/plosone/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.