Stability analysis of polynomials with an approach of differential topology.
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| Title: | Stability analysis of polynomials with an approach of differential topology. |
|---|---|
| Authors: | López‐Flores, Eleazar1 (AUTHOR), Aguirre‐Hernández, Baltazar1 (AUTHOR) bahe@xanum.uam.mx, Frías‐Armenta, Martín Eduardo2 (AUTHOR) |
| Source: | Asian Journal of Control. Mar2025, Vol. 27 Issue 2, p1068-1074. 7p. |
| Subjects: | Hurwitz polynomials, Differential topology, Polynomials, Fibers |
| Abstract: | Summary: In this paper, we study the Hurwitz stability of polynomials. By considering that a 2m−$$ 2m- $$degree Hurwitz polynomial has its corresponding Markov parameters, we define the set Hankel2m$$ {Hankel}_{2m} $$ in Section 3, we also define Hankel2m−1$$ {Hankel}_{2m-1} $$. Based on properties of the Hankel matrices and the stability test, as well as by using ideas of differential topology, we show that Hankel2m$$ {Hankel}_{2m} $$ is a fiber bundle with a Hankel2m−1$$ {Hankel}_{2m-1} $$ base. This result allows us to obtain an interesting application: Given a Hurwitz polynomial, we can generate two families of positive definite Hankel matrices. [ABSTRACT FROM AUTHOR] |
| Copyright of Asian Journal of Control is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
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| Header | DbId: egs DbLabel: Engineering Source An: 183919408 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Stability analysis of polynomials with an approach of differential topology. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22López‐Flores%2C+Eleazar%22">López‐Flores, Eleazar</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Aguirre‐Hernández%2C+Baltazar%22">Aguirre‐Hernández, Baltazar</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> bahe@xanum.uam.mx</i><br /><searchLink fieldCode="AR" term="%22Frías‐Armenta%2C+Martín+Eduardo%22">Frías‐Armenta, Martín Eduardo</searchLink><relatesTo>2</relatesTo> (AUTHOR) – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Asian+Journal+of+Control%22">Asian Journal of Control</searchLink>. Mar2025, Vol. 27 Issue 2, p1068-1074. 7p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Hurwitz+polynomials%22">Hurwitz polynomials</searchLink><br /><searchLink fieldCode="DE" term="%22Differential+topology%22">Differential topology</searchLink><br /><searchLink fieldCode="DE" term="%22Polynomials%22">Polynomials</searchLink><br /><searchLink fieldCode="DE" term="%22Fibers%22">Fibers</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Summary: In this paper, we study the Hurwitz stability of polynomials. By considering that a 2m−$$ 2m- $$degree Hurwitz polynomial has its corresponding Markov parameters, we define the set Hankel2m$$ {Hankel}_{2m} $$ in Section 3, we also define Hankel2m−1$$ {Hankel}_{2m-1} $$. Based on properties of the Hankel matrices and the stability test, as well as by using ideas of differential topology, we show that Hankel2m$$ {Hankel}_{2m} $$ is a fiber bundle with a Hankel2m−1$$ {Hankel}_{2m-1} $$ base. This result allows us to obtain an interesting application: Given a Hurwitz polynomial, we can generate two families of positive definite Hankel matrices. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Asian Journal of Control is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1002/asjc.3476 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 7 StartPage: 1068 Subjects: – SubjectFull: Hurwitz polynomials Type: general – SubjectFull: Differential topology Type: general – SubjectFull: Polynomials Type: general – SubjectFull: Fibers Type: general Titles: – TitleFull: Stability analysis of polynomials with an approach of differential topology. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: López‐Flores, Eleazar – PersonEntity: Name: NameFull: Aguirre‐Hernández, Baltazar – PersonEntity: Name: NameFull: Frías‐Armenta, Martín Eduardo IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 03 Text: Mar2025 Type: published Y: 2025 Identifiers: – Type: issn-print Value: 15618625 Numbering: – Type: volume Value: 27 – Type: issue Value: 2 Titles: – TitleFull: Asian Journal of Control Type: main |
| ResultId | 1 |
