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

Noé Martínez, Luis E. Garza and Gerardo Romero ()
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Noé Martínez: Unidad Académica Multidisciplinaria Reynosa Rodhe, Universidad Autónoma de Tamaulipas, Reynosa C.P. 88779, Mexico
Luis E. Garza: Facultad de Ciencias, Universidad de Colima, Colima C.P. 28040, Mexico
Gerardo Romero: Unidad Académica Multidisciplinaria Reynosa Rodhe, Universidad Autónoma de Tamaulipas, Reynosa C.P. 88779, Mexico

Mathematics, 2023, vol. 11, issue 20, 1-12

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.

Keywords: robust stability; Schur polynomials; orthogonal polynomials; Rouché’s theorem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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