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

Autor:	Noé Martínez, Luis E. Garza, Gerardo Romero
Jazyk:	angličtina
Rok vydání:	2023
Předmět:	robust stability Schur polynomials orthogonal polynomials Rouché’s theorem Mathematics QA1-939
Zdroj:	Mathematics, Vol 11, Iss 20, p 4244 (2023)
Druh dokumentu:	article
ISSN:	2227-7390
DOI:	10.3390/math11204244
Popis:	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.
Databáze:	Directory of Open Access Journals
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