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

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 p...
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Autor*in:	Noé Martínez [verfasserIn] Luis E. Garza [verfasserIn] Gerardo Romero [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2023

Schlagwörter:	robust stability Schur polynomials orthogonal polynomials Rouché’s theorem

Übergeordnetes Werk:	In: Mathematics - MDPI AG, 2013, 11(2023), 4244, p 4244
Übergeordnetes Werk:	volume:11 ; year:2023 ; number:4244, p 4244

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc

DOI / URN:	10.3390/math11204244

Katalog-ID:	DOAJ093112017

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callnumber-first	Q - Science
author	Noé Martínez
spellingShingle	Noé Martínez misc QA1-939 misc robust stability misc Schur polynomials misc orthogonal polynomials misc Rouché’s theorem misc Mathematics An Application of Rouché’s Theorem to Delimit the Zeros of a Certain Class of Robustly Stable Polynomials
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topic_title	QA1-939 An Application of Rouché’s Theorem to Delimit the Zeros of a Certain Class of Robustly Stable Polynomials robust stability Schur polynomials orthogonal polynomials Rouché’s theorem
topic	misc QA1-939 misc robust stability misc Schur polynomials misc orthogonal polynomials misc Rouché’s theorem misc Mathematics
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title	An Application of Rouché’s Theorem to Delimit the Zeros of a Certain Class of Robustly Stable Polynomials
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title_full	An Application of Rouché’s Theorem to Delimit the Zeros of a Certain Class of Robustly Stable Polynomials
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title_sort	application of rouché’s theorem to delimit the zeros of a certain class of robustly stable polynomials
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title_auth	An Application of Rouché’s Theorem to Delimit the Zeros of a Certain Class of Robustly Stable Polynomials
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.
abstractGer	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.
abstract_unstemmed	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.
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title_short	An Application of Rouché’s Theorem to Delimit the Zeros of a Certain Class of Robustly Stable Polynomials
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