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. |
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| 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] |
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| Database: | Engineering Source |
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| 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] |
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| ISSN: | 15618625 |
| DOI: | 10.1002/asjc.3476 |
