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Asymptotic Analysis of Multiple Characteristics Roots for Quasi-polynomials of Retarded-Type

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Delays and Interconnections: Methodology, Algorithms and Applications

Part of the book series: Advances in Delays and Dynamics ((ADVSDD,volume 10))

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Abstract

In this chapter, the analysis of the behavior of multiple critical roots with respect to the delay parameters for a class of quasi-polynomials is addressed. The analysis is based on the construction of the so-called Weierstrass polynomial. Several numerical examples encountered in the control literature are considered to illustrate the proposed approach.

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Acknowledgements

The research of J. Chen was supported in part by the Hong Kong RGC under Projects F-HK006/11T and CityU 11260016; the work of A. Martínez-González was financially supported by CONACyT, Mexico.

Author information

Authors and Affiliations

  1. Universidad Autónoma de San Luis Potosí (UASLP), Facultad de Ingeniería, Dr. Manuel Nava No. 8, Zona Universitaria, 78290, San Luis Potosí, S.L.P., Mexico

    A. Martínez-González, C. F. Méndez-Barrios & G. Mejía-Rodríguez

  2. Laboratoire des Signaux et Systèmes (L2S, UMR CNRS 8506), CNRS-Supélec 3, rue Joliot Curie, 91192, Gif-sur-Yvette, France

    S.-I. Niculescu

  3. Department of Electronic Engineering, City University of Hong Kong, Hong Kong, China

    J. Chen

  4. Departamento Académico de Sistemas Digitales ITAM, Río Hondo 1, 01080, Ciudad de México, Mexico

    J. G. Romero

Authors
  1. A. Martínez-González
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  2. S.-I. Niculescu
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  3. J. Chen
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  4. C. F. Méndez-Barrios
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  5. J. G. Romero
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  6. G. Mejía-Rodríguez
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Corresponding author

Correspondence to C. F. Méndez-Barrios .

Editor information

Editors and Affiliations

  1. Laboratoire des Signaux et Systèmes, CNRS-CentraleSupèlec-Université Paris-Saclay, Gif-sur-Yvette, France

    Giorgio Valmorbida

  2. Laboratoire d’Analyse et d’Architecture de Systèmes-CNRS, Toulouse, France

    Alexandre Seuret

  3. Laboratoire des Signaux et Systèmes, CNRS-CentraleSupèlec-Université Paris-Saclay, Gif-sur-Yvette, France

    Islam Boussaada

  4. Mechanical and Industrial Engineering, Northeastern University, Boston, MA, USA

    Rifat Sipahi

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Martínez-González, A., Niculescu, SI., Chen, J., Méndez-Barrios, C.F., Romero, J.G., Mejía-Rodríguez, G. (2019). Asymptotic Analysis of Multiple Characteristics Roots for Quasi-polynomials of Retarded-Type. In: Valmorbida, G., Seuret, A., Boussaada, I., Sipahi, R. (eds) Delays and Interconnections: Methodology, Algorithms and Applications. Advances in Delays and Dynamics, vol 10. Springer, Cham. https://doi.org/10.1007/978-3-030-11554-8_9

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