Stability and distance to instability for polynomial matrix families. Complex perturbations

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Stability and distance to instability for polynomial matrix families. Complex perturbations. / Kalinina, Elizaveta A.; Smol'kin, Yurii A.; Uteshev, Alexei Yu.

в: Linear and Multilinear Algebra, Том 70, № 7, 2022, стр. 1291 - 1314.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

BibTeX

@article{a7ca35e55f494b788681f1f42c90d06b,

title = "Stability and distance to instability for polynomial matrix families. Complex perturbations",

abstract = "For a family of real matrices with entries polynomially depending on parameters, symbolic algorithms are proposed for verification of the Routh–Hurwitz stability under parameter variations in a given box, and for the distance to instability computation in the case of perturbations over (Formula presented.). Both problems are reduced to the analysis of real zeros of a pair of univariate polynomials; one of these reductions is based on the discriminant computation in the Hankel determinant form. We also discuss a potential application of the suggested approach for finding an estimation for the accuracy of the distance to instability computations via numerical procedures.",

keywords = "discriminant, distance to instability, Polynomial matrix, stability of a matrix, APPROXIMATION, ROBUST STABILITY, ALGORITHM, SYSTEMS, H-INFINITY-NORM",

author = "Kalinina, {Elizaveta A.} and Smol'kin, {Yurii A.} and Uteshev, {Alexei Yu}",

note = "Publisher Copyright: {\textcopyright} 2020 Informa UK Limited, trading as Taylor & Francis Group.",

year = "2022",

doi = "10.1080/03081087.2020.1759500",

language = "English",

volume = "70",

pages = "1291 -- 1314",

journal = "Linear and Multilinear Algebra",

issn = "0308-1087",

publisher = "Taylor & Francis",

number = "7",

}

RIS

TY - JOUR

T1 - Stability and distance to instability for polynomial matrix families. Complex perturbations

AU - Kalinina, Elizaveta A.

AU - Smol'kin, Yurii A.

AU - Uteshev, Alexei Yu

PY - 2022

Y1 - 2022

N2 - For a family of real matrices with entries polynomially depending on parameters, symbolic algorithms are proposed for verification of the Routh–Hurwitz stability under parameter variations in a given box, and for the distance to instability computation in the case of perturbations over (Formula presented.). Both problems are reduced to the analysis of real zeros of a pair of univariate polynomials; one of these reductions is based on the discriminant computation in the Hankel determinant form. We also discuss a potential application of the suggested approach for finding an estimation for the accuracy of the distance to instability computations via numerical procedures.

AB - For a family of real matrices with entries polynomially depending on parameters, symbolic algorithms are proposed for verification of the Routh–Hurwitz stability under parameter variations in a given box, and for the distance to instability computation in the case of perturbations over (Formula presented.). Both problems are reduced to the analysis of real zeros of a pair of univariate polynomials; one of these reductions is based on the discriminant computation in the Hankel determinant form. We also discuss a potential application of the suggested approach for finding an estimation for the accuracy of the distance to instability computations via numerical procedures.

KW - discriminant

KW - distance to instability

KW - Polynomial matrix

KW - stability of a matrix

KW - APPROXIMATION

KW - ROBUST STABILITY

KW - ALGORITHM

KW - SYSTEMS

KW - H-INFINITY-NORM

UR - http://www.scopus.com/inward/record.url?scp=85084359000&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/58bfc5d4-cd4a-3b56-9ba1-9ebc997bb7d6/

U2 - 10.1080/03081087.2020.1759500

DO - 10.1080/03081087.2020.1759500

M3 - Article

AN - SCOPUS:85084359000

VL - 70

SP - 1291

EP - 1314

JO - Linear and Multilinear Algebra

JF - Linear and Multilinear Algebra

SN - 0308-1087

IS - 7

ER -

ID: 53522114