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An Application of Rouché’s Theorem to Delimit the Zeros of a Certain Class of Robustly Stable Polynomials

Author

Listed:
  • Noé Martínez

    (Unidad Académica Multidisciplinaria Reynosa Rodhe, Universidad Autónoma de Tamaulipas, Reynosa C.P. 88779, Mexico
    These authors contributed equally to this work.)

  • Luis E. Garza

    (Facultad de Ciencias, Universidad de Colima, Colima C.P. 28040, Mexico
    These authors contributed equally to this work.)

  • Gerardo Romero

    (Unidad Académica Multidisciplinaria Reynosa Rodhe, Universidad Autónoma de Tamaulipas, Reynosa C.P. 88779, Mexico
    These authors contributed equally to this work.)

Abstract

An important problem related to the study of the robust stability of a linear system that presents variation in terms of an uncertain parameter consists of understanding the variation in the roots of a system’s characteristic polynomial in terms of the uncertain parameter. In this contribution, we propose an algorithm to provide sufficient conditions on the uncertain parameter in such a way that a robustly stable family of polynomials has all of its zeros inside a specific subset of its stability region. Our method is based on the Rouché’s theorem and uses robustly stable polynomials constructed by using basic properties of orthogonal polynomials.

Suggested Citation

  • Noé Martínez & Luis E. Garza & Gerardo Romero, 2023. "An Application of Rouché’s Theorem to Delimit the Zeros of a Certain Class of Robustly Stable Polynomials," Mathematics, MDPI, vol. 11(20), pages 1-12, October.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:20:p:4244-:d:1257551
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    References listed on IDEAS

    as
    1. Alejandro Arceo & Héctor F. Flores & Lino G. Garza & Luis E. Garza & Gerardo Romero & Alejandro F. Villaverde, 2022. "On Robust Stability for Hurwitz Polynomials via Recurrence Relations and Linear Combinations of Orthogonal Polynomials," Complexity, Hindawi, vol. 2022, pages 1-13, March.
    2. Alejandro Arceo & Luis E. Garza & Gerardo Romero, 2019. "Robust Stability of Hurwitz Polynomials Associated with Modified Classical Weights," Mathematics, MDPI, vol. 7(9), pages 1-20, September.
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