Even degree polynomials with roots on the unit circle and Segments of Schur polynomials

Baltazar Aguirre-Hernández; Ricardo García; Horacio Leyva; Julio Solís-Daun; Francisco A. Carrillo; Rodolfo Suárez

doi:10.3182/20120620-3-DK-2025.00012

Even degree polynomials with roots on the unit circle and Segments of Schur polynomials

Baltazar Aguirre-Hernández^*, Ricardo García, Horacio Leyva, Julio Solís-Daun, Francisco A. Carrillo, Rodolfo Suárez

^*Corresponding author for this work

Departamento de Matemáticas

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

In this paper we study a kind of even degree polynomials of a special form. Necessary and sufficient conditions are given in order to decide if such polynomials have all their roots on the unit circle. Next, we apply these results to obtain sufficient conditions to have the Schur stability of a segment of polynomials.

Original language	English
Title of host publication	ROCOND'12 - 7th IFAC Symposium on Robust Control Design
Publisher	IFAC Secretariat
Pages	174-177
Number of pages	4
Edition	PART 1
ISBN (Print)	9783902823038
DOIs	https://doi.org/10.3182/20120620-3-DK-2025.00012
State	Published - 2012
Event	7th IFAC Symposium on Robust Control Design, ROCOND'12 - Aalborg, Denmark Duration: 20 Jun 2012 → 22 Jun 2012

Publication series

Name	IFAC Proceedings Volumes (IFAC-PapersOnline)
Number	PART 1
Volume	7
ISSN (Print)	1474-6670

Conference

Conference	7th IFAC Symposium on Robust Control Design, ROCOND'12
Country/Territory	Denmark
City	Aalborg
Period	20/06/12 → 22/06/12

Keywords

Roots of polynomials
Schur polynomials
Segments of Schur poynomials

Access to Document

10.3182/20120620-3-DK-2025.00012

Cite this

Aguirre-Hernández, B., García, R., Leyva, H., Solís-Daun, J., Carrillo, F. A., & Suárez, R. (2012). Even degree polynomials with roots on the unit circle and Segments of Schur polynomials. In ROCOND'12 - 7th IFAC Symposium on Robust Control Design (PART 1 ed., pp. 174-177). (IFAC Proceedings Volumes (IFAC-PapersOnline); Vol. 7, No. PART 1). IFAC Secretariat. https://doi.org/10.3182/20120620-3-DK-2025.00012

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title = "Even degree polynomials with roots on the unit circle and Segments of Schur polynomials",

abstract = "In this paper we study a kind of even degree polynomials of a special form. Necessary and sufficient conditions are given in order to decide if such polynomials have all their roots on the unit circle. Next, we apply these results to obtain sufficient conditions to have the Schur stability of a segment of polynomials.",

keywords = "Roots of polynomials, Schur polynomials, Segments of Schur poynomials",

author = "Baltazar Aguirre-Hern{\'a}ndez and Ricardo Garc{\'i}a and Horacio Leyva and Julio Sol{\'i}s-Daun and Carrillo, {Francisco A.} and Rodolfo Su{\'a}rez",

year = "2012",

doi = "10.3182/20120620-3-DK-2025.00012",

language = "Ingl{\'e}s",

isbn = "9783902823038",

series = "IFAC Proceedings Volumes (IFAC-PapersOnline)",

publisher = "IFAC Secretariat",

number = "PART 1",

pages = "174--177",

booktitle = "ROCOND'12 - 7th IFAC Symposium on Robust Control Design",

edition = "PART 1",

note = "7th IFAC Symposium on Robust Control Design, ROCOND'12 ; Conference date: 20-06-2012 Through 22-06-2012",

}

Aguirre-Hernández, B, García, R, Leyva, H, Solís-Daun, J, Carrillo, FA & Suárez, R 2012, Even degree polynomials with roots on the unit circle and Segments of Schur polynomials. in ROCOND'12 - 7th IFAC Symposium on Robust Control Design. PART 1 edn, IFAC Proceedings Volumes (IFAC-PapersOnline), no. PART 1, vol. 7, IFAC Secretariat, pp. 174-177, 7th IFAC Symposium on Robust Control Design, ROCOND'12, Aalborg, Denmark, 20/06/12. https://doi.org/10.3182/20120620-3-DK-2025.00012

Even degree polynomials with roots on the unit circle and Segments of Schur polynomials. / Aguirre-Hernández, Baltazar; García, Ricardo; Leyva, Horacio et al.
ROCOND'12 - 7th IFAC Symposium on Robust Control Design. PART 1. ed. IFAC Secretariat, 2012. p. 174-177 (IFAC Proceedings Volumes (IFAC-PapersOnline); Vol. 7, No. PART 1).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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T1 - Even degree polynomials with roots on the unit circle and Segments of Schur polynomials

AU - Aguirre-Hernández, Baltazar

AU - García, Ricardo

AU - Leyva, Horacio

AU - Solís-Daun, Julio

AU - Carrillo, Francisco A.

AU - Suárez, Rodolfo

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AB - In this paper we study a kind of even degree polynomials of a special form. Necessary and sufficient conditions are given in order to decide if such polynomials have all their roots on the unit circle. Next, we apply these results to obtain sufficient conditions to have the Schur stability of a segment of polynomials.

KW - Roots of polynomials

KW - Schur polynomials

KW - Segments of Schur poynomials

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M3 - Contribución a la conferencia

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ER -

Aguirre-Hernández B, García R, Leyva H, Solís-Daun J, Carrillo FA, Suárez R. Even degree polynomials with roots on the unit circle and Segments of Schur polynomials. In ROCOND'12 - 7th IFAC Symposium on Robust Control Design. PART 1 ed. IFAC Secretariat. 2012. p. 174-177. (IFAC Proceedings Volumes (IFAC-PapersOnline); PART 1). doi: 10.3182/20120620-3-DK-2025.00012

Even degree polynomials with roots on the unit circle and Segments of Schur polynomials

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Keywords

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