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Analytic Curve Frequency-Sweeping Stability Tests for Systems with Commensurate Delays pp 35–46Cite as

Computing Puiseux Series for a Critical Pair

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Abstract

In this chapter, we first explain why the existing methods for describing the asymptotic behavior do not work in the general case. Next, we present an algorithm for calculating all the first-order terms of the Puiseux series. Furthermore, we show that the proposed approach can be used to obtain higher order terms of the Puiseux series in order to study appropriately the degenerate case. Finally, some useful properties on the Puiseux series are presented.

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Notes

  1. 1.

    The theorem as well as the proof will be given in Chap. 7.

  2. 2.

    Example 4.7 is specific as there is an invariant characteristic root at the origin.

  3. 3.

    The earlier conference versions of the work were reported in [17, 33].

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Authors and Affiliations

  1. School of Information Science and Engineering, Northeastern University, Shenyang, Liaoning, China

    Xu-Guang Li

  2. Laboratoire des Signaux et Systèmes (L2S, UMR CNRS 8506), CNRS-CentraleSupélec-Université Paris-Sud, Gif-Sur-Yvette, France

    Silviu-Iulian Niculescu

  3. Department of Computer Science and Telecommunication, UPE, ESIEE Paris, Noisy-le-Grand, France

    Arben Çela

Authors
  1. Xu-Guang Li
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  2. Silviu-Iulian Niculescu
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  3. Arben Çela
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Correspondence to Xu-Guang Li .

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Li, XG., Niculescu, SI., Çela, A. (2015). Computing Puiseux Series for a Critical Pair. In: Analytic Curve Frequency-Sweeping Stability Tests for Systems with Commensurate Delays. SpringerBriefs in Electrical and Computer Engineering(). Springer, Cham. https://doi.org/10.1007/978-3-319-15717-7_4

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  • DOI: https://doi.org/10.1007/978-3-319-15717-7_4

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-15716-0

  • Online ISBN: 978-3-319-15717-7

  • eBook Packages: EngineeringEngineering (R0)

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