Robust D-stability via positivity

D. D. Šiljak; D. M. Stipanović

doi:10.1109/ACC.1998.703085

Robust D-stability via positivity

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

Abstract

The main objective of this paper is to convert the general problem of robust D-stability of a complex polynomial to positivity in the real domain of the corresponding magnitude function. In particular, the obtained Hurwitz stability criterion is applied to polynomials with interval parameters and polynomic uncertainty structures. The robust stability is verified by testing positivity of a real polynomial using the Bernstein subdivision algorithm. A new feature in this context is the stopping criterion, which is applied whenever the algorithm is inconclusive after a large number of iterations, but we can show that at least one zero of the polynomial is closer to the imaginary axis than a prescribed limit.

Original language	English (US)
Title of host publication	Proceedings of the 1998 American Control Conference, ACC 1998
Pages	2502-2509
Number of pages	8
DOIs	https://doi.org/10.1109/ACC.1998.703085
State	Published - 1998
Externally published	Yes
Event	1998 American Control Conference, ACC 1998 - Philadelphia, PA, United States Duration: Jun 24 1998 → Jun 26 1998

Publication series

Name	Proceedings of the American Control Conference
Volume	4
ISSN (Print)	0743-1619

Other

Other	1998 American Control Conference, ACC 1998
Country/Territory	United States
City	Philadelphia, PA
Period	6/24/98 → 6/26/98

ASJC Scopus subject areas

Electrical and Electronic Engineering

Online availability

10.1109/ACC.1998.703085

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title = "Robust D-stability via positivity",

abstract = "The main objective of this paper is to convert the general problem of robust D-stability of a complex polynomial to positivity in the real domain of the corresponding magnitude function. In particular, the obtained Hurwitz stability criterion is applied to polynomials with interval parameters and polynomic uncertainty structures. The robust stability is verified by testing positivity of a real polynomial using the Bernstein subdivision algorithm. A new feature in this context is the stopping criterion, which is applied whenever the algorithm is inconclusive after a large number of iterations, but we can show that at least one zero of the polynomial is closer to the imaginary axis than a prescribed limit.",

author = "{\v S}iljak, {D. D.} and Stipanovi{\'c}, {D. M.}",

note = "Funding Information: This work has been supported by the National Science Foundation under the grant ECS-9526142.; 1998 American Control Conference, ACC 1998 ; Conference date: 24-06-1998 Through 26-06-1998",

year = "1998",

doi = "10.1109/ACC.1998.703085",

language = "English (US)",

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series = "Proceedings of the American Control Conference",

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AU - Šiljak, D. D.

AU - Stipanović, D. M.

N1 - Funding Information: This work has been supported by the National Science Foundation under the grant ECS-9526142.

PY - 1998

Y1 - 1998

N2 - The main objective of this paper is to convert the general problem of robust D-stability of a complex polynomial to positivity in the real domain of the corresponding magnitude function. In particular, the obtained Hurwitz stability criterion is applied to polynomials with interval parameters and polynomic uncertainty structures. The robust stability is verified by testing positivity of a real polynomial using the Bernstein subdivision algorithm. A new feature in this context is the stopping criterion, which is applied whenever the algorithm is inconclusive after a large number of iterations, but we can show that at least one zero of the polynomial is closer to the imaginary axis than a prescribed limit.

AB - The main objective of this paper is to convert the general problem of robust D-stability of a complex polynomial to positivity in the real domain of the corresponding magnitude function. In particular, the obtained Hurwitz stability criterion is applied to polynomials with interval parameters and polynomic uncertainty structures. The robust stability is verified by testing positivity of a real polynomial using the Bernstein subdivision algorithm. A new feature in this context is the stopping criterion, which is applied whenever the algorithm is inconclusive after a large number of iterations, but we can show that at least one zero of the polynomial is closer to the imaginary axis than a prescribed limit.

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DO - 10.1109/ACC.1998.703085

M3 - Conference contribution

AN - SCOPUS:84881350240

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SN - 9780780345300

T3 - Proceedings of the American Control Conference

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EP - 2509

BT - Proceedings of the 1998 American Control Conference, ACC 1998

T2 - 1998 American Control Conference, ACC 1998

Y2 - 24 June 1998 through 26 June 1998

ER -

Robust D-stability via positivity

Abstract

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