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...
Ausführliche Beschreibung
Autor*in: |
Noé Martínez [verfasserIn] Luis E. Garza [verfasserIn] Gerardo Romero [verfasserIn] |
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E-Artikel |
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Sprache: |
Englisch |
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2023 |
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In: Mathematics - MDPI AG, 2013, 11(2023), 4244, p 4244 |
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Übergeordnetes Werk: |
volume:11 ; year:2023 ; number:4244, p 4244 |
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DOI / URN: |
10.3390/math11204244 |
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Katalog-ID: |
DOAJ093112017 |
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10.3390/math11204244 doi (DE-627)DOAJ093112017 (DE-599)DOAJa8cb227923864389a9d6dad1096755af DE-627 ger DE-627 rakwb eng QA1-939 Noé Martínez verfasserin aut An Application of Rouché’s Theorem to Delimit the Zeros of a Certain Class of Robustly Stable Polynomials 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier 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. robust stability Schur polynomials orthogonal polynomials Rouché’s theorem Mathematics Luis E. Garza verfasserin aut Gerardo Romero verfasserin aut In Mathematics MDPI AG, 2013 11(2023), 4244, p 4244 (DE-627)737287764 (DE-600)2704244-3 22277390 nnns volume:11 year:2023 number:4244, p 4244 https://doi.org/10.3390/math11204244 kostenfrei https://doaj.org/article/a8cb227923864389a9d6dad1096755af kostenfrei https://www.mdpi.com/2227-7390/11/20/4244 kostenfrei https://doaj.org/toc/2227-7390 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 11 2023 4244, p 4244 |
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10.3390/math11204244 doi (DE-627)DOAJ093112017 (DE-599)DOAJa8cb227923864389a9d6dad1096755af DE-627 ger DE-627 rakwb eng QA1-939 Noé Martínez verfasserin aut An Application of Rouché’s Theorem to Delimit the Zeros of a Certain Class of Robustly Stable Polynomials 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier 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. robust stability Schur polynomials orthogonal polynomials Rouché’s theorem Mathematics Luis E. Garza verfasserin aut Gerardo Romero verfasserin aut In Mathematics MDPI AG, 2013 11(2023), 4244, p 4244 (DE-627)737287764 (DE-600)2704244-3 22277390 nnns volume:11 year:2023 number:4244, p 4244 https://doi.org/10.3390/math11204244 kostenfrei https://doaj.org/article/a8cb227923864389a9d6dad1096755af kostenfrei https://www.mdpi.com/2227-7390/11/20/4244 kostenfrei https://doaj.org/toc/2227-7390 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 11 2023 4244, p 4244 |
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10.3390/math11204244 doi (DE-627)DOAJ093112017 (DE-599)DOAJa8cb227923864389a9d6dad1096755af DE-627 ger DE-627 rakwb eng QA1-939 Noé Martínez verfasserin aut An Application of Rouché’s Theorem to Delimit the Zeros of a Certain Class of Robustly Stable Polynomials 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier 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. robust stability Schur polynomials orthogonal polynomials Rouché’s theorem Mathematics Luis E. Garza verfasserin aut Gerardo Romero verfasserin aut In Mathematics MDPI AG, 2013 11(2023), 4244, p 4244 (DE-627)737287764 (DE-600)2704244-3 22277390 nnns volume:11 year:2023 number:4244, p 4244 https://doi.org/10.3390/math11204244 kostenfrei https://doaj.org/article/a8cb227923864389a9d6dad1096755af kostenfrei https://www.mdpi.com/2227-7390/11/20/4244 kostenfrei https://doaj.org/toc/2227-7390 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 11 2023 4244, p 4244 |
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10.3390/math11204244 doi (DE-627)DOAJ093112017 (DE-599)DOAJa8cb227923864389a9d6dad1096755af DE-627 ger DE-627 rakwb eng QA1-939 Noé Martínez verfasserin aut An Application of Rouché’s Theorem to Delimit the Zeros of a Certain Class of Robustly Stable Polynomials 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier 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. robust stability Schur polynomials orthogonal polynomials Rouché’s theorem Mathematics Luis E. Garza verfasserin aut Gerardo Romero verfasserin aut In Mathematics MDPI AG, 2013 11(2023), 4244, p 4244 (DE-627)737287764 (DE-600)2704244-3 22277390 nnns volume:11 year:2023 number:4244, p 4244 https://doi.org/10.3390/math11204244 kostenfrei https://doaj.org/article/a8cb227923864389a9d6dad1096755af kostenfrei https://www.mdpi.com/2227-7390/11/20/4244 kostenfrei https://doaj.org/toc/2227-7390 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 11 2023 4244, p 4244 |
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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 |
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An Application of Rouché’s Theorem to Delimit the Zeros of a Certain Class of Robustly Stable Polynomials |
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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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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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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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|
score |
7.399544 |