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Doklady Mathematics

, Volume 97, Issue 3, pp 203–206 | Cite as

Transformation of Time-Delay Systems to a Form with Zero Dynamics

  • A. V. Il’inEmail author
  • E. I. Atamas’
  • V. V. Fomichev
Mathematics

Abstract

The problem of transforming a controlled linear stationary system of differential equations with commensurable time delays into a canonical form with zero dynamics is considered. This problem has been well studied for ODE systems and is closely related to the concept of a relative degree. In this paper, the results are extended to time-delay systems.

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References

  1. 1.
    S. K. Korovin, A. V. Il’in, and V. V. Fomichev, Dokl. Math. 75 (3), 467–471 (2007).MathSciNetCrossRefGoogle Scholar
  2. 2.
    A. V. Il’in, S. K. Korovin, and V. V. Fomichev, Differ. Equations 42 (12), 1696–1706 (2006).MathSciNetCrossRefGoogle Scholar
  3. 3.
    A. I. Rogovskii, A. V. Kraev, and V. V. Fomichev, Vestn. Mosk. Univ. Ser. 15: Vychisl. Mat. Kibern., No. 3, 20–26 (2015).Google Scholar
  4. 4.
    V. V. Fomichev, A. V. Kraev, and A. I. Rogovskii, Differ. Equations 52 (8), 1061–1071 (2016).MathSciNetCrossRefGoogle Scholar
  5. 5.
    V. V. Fomichev, A. V. Kraev, and A. I. Rogovskiy, Differ. Equations 53 (5), 686–708 (2017).MathSciNetCrossRefGoogle Scholar
  6. 6.
    E. I. Atamas’, A. V. Il’in, and V. V. Fomichev, Differ. Equations 49 (11), 1329–1335 (2013).MathSciNetCrossRefGoogle Scholar
  7. 7.
    A. Isidori, Nonlinear Control Systems (Springer-Verlag, New York, 1997).zbMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  • A. V. Il’in
    • 1
    • 2
    • 3
    Email author
  • E. I. Atamas’
    • 2
  • V. V. Fomichev
    • 1
    • 2
    • 3
    • 4
  1. 1.Department of Mathematics, School of ScienceHangzhou Dianzi UniversityHangzhouChina
  2. 2.Faculty of Computational Mathematics and CyberneticsMoscow State UniversityMoscowRussia
  3. 3.Center of Information Technologies in DesignRussian Academy of SciencesOdintsovo, Moscow oblastRussia
  4. 4.Trapeznikov Institute of Control SciencesRussian Academy of SciencesMoscowRussia

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