CLASS OF STABILITY REGIONS FOR WHICH A KHARITONOV LIKE THEOREM HOLDS.

Ian R. Petersen

doi:10.1109/CDC.1987.272857

CLASS OF STABILITY REGIONS FOR WHICH A KHARITONOV LIKE THEOREM HOLDS.

Ian R. Petersen^*

^*Corresponding author for this work

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

12 Citations (Scopus)

Abstract

Families of complex polynomials with coefficients lying within given intervals are considered. In particular, the problem of determining if all polynomials in a family have the property that all of their roots lie in a given region is treated. The notion of a 'Kharitonov region' is defined. Roughly speaking a Kharitonov region is a region in the complex plane with the following property: Given any suitable family of polynomials, in order to determine if all polynomials in the family have all their roots in the region, it suffices to check only the vertex polynomials of the family. The author's main result is a sufficient condition for a given region to be a Kharitonov region.

Original language	English
Title of host publication	Proceedings of the 26th IEEE Conference on Decision and Control
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	440-444
Number of pages	5
Volume	1
DOIs	https://doi.org/10.1109/CDC.1987.272857
Publication status	Published - 1987
Externally published	Yes
Event	26th IEEE Conference on Decision and Control - Westin Century-Plaza Hotel, Los Angeles, California, United States Duration: 9 Dec 1987 → 11 Dec 1987 Conference number: 11384 https://ieeexplore.ieee.org/xpl/conhome/4049207/proceeding

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
Publisher	Institute of Electrical and Electronics Engineers Inc.
ISSN (Print)	0191-2216

Conference

Conference	26th IEEE Conference on Decision and Control
Country/Territory	United States
City	Los Angeles, California
Period	9/12/87 → 11/12/87
Internet address	https://ieeexplore.ieee.org/xpl/conhome/4049207/proceeding

Access to Document

10.1109/CDC.1987.272857

Cite this

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title = "CLASS OF STABILITY REGIONS FOR WHICH A KHARITONOV LIKE THEOREM HOLDS.",

abstract = "Families of complex polynomials with coefficients lying within given intervals are considered. In particular, the problem of determining if all polynomials in a family have the property that all of their roots lie in a given region is treated. The notion of a 'Kharitonov region' is defined. Roughly speaking a Kharitonov region is a region in the complex plane with the following property: Given any suitable family of polynomials, in order to determine if all polynomials in the family have all their roots in the region, it suffices to check only the vertex polynomials of the family. The author's main result is a sufficient condition for a given region to be a Kharitonov region.",

author = "Petersen, \{Ian R.\}",

year = "1987",

doi = "10.1109/CDC.1987.272857",

language = "English",

volume = "1",

series = "Proceedings of the IEEE Conference on Decision and Control",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

pages = "440--444",

booktitle = "Proceedings of the 26th IEEE Conference on Decision and Control",

address = "United States",

note = "26th IEEE Conference on Decision and Control ; Conference date: 09-12-1987 Through 11-12-1987",

url = "https://ieeexplore.ieee.org/xpl/conhome/4049207/proceeding",

}

Petersen, IR 1987, CLASS OF STABILITY REGIONS FOR WHICH A KHARITONOV LIKE THEOREM HOLDS. in Proceedings of the 26th IEEE Conference on Decision and Control . vol. 1, Proceedings of the IEEE Conference on Decision and Control, Institute of Electrical and Electronics Engineers Inc., pp. 440-444, 26th IEEE Conference on Decision and Control , Los Angeles, California, United States, 9/12/87. https://doi.org/10.1109/CDC.1987.272857

CLASS OF STABILITY REGIONS FOR WHICH A KHARITONOV LIKE THEOREM HOLDS. / Petersen, Ian R.
Proceedings of the 26th IEEE Conference on Decision and Control . Vol. 1 Institute of Electrical and Electronics Engineers Inc., 1987. p. 440-444 (Proceedings of the IEEE Conference on Decision and Control).

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

TY - GEN

T1 - CLASS OF STABILITY REGIONS FOR WHICH A KHARITONOV LIKE THEOREM HOLDS.

AU - Petersen, Ian R.

N1 - Conference code: 11384

PY - 1987

Y1 - 1987

N2 - Families of complex polynomials with coefficients lying within given intervals are considered. In particular, the problem of determining if all polynomials in a family have the property that all of their roots lie in a given region is treated. The notion of a 'Kharitonov region' is defined. Roughly speaking a Kharitonov region is a region in the complex plane with the following property: Given any suitable family of polynomials, in order to determine if all polynomials in the family have all their roots in the region, it suffices to check only the vertex polynomials of the family. The author's main result is a sufficient condition for a given region to be a Kharitonov region.

AB - Families of complex polynomials with coefficients lying within given intervals are considered. In particular, the problem of determining if all polynomials in a family have the property that all of their roots lie in a given region is treated. The notion of a 'Kharitonov region' is defined. Roughly speaking a Kharitonov region is a region in the complex plane with the following property: Given any suitable family of polynomials, in order to determine if all polynomials in the family have all their roots in the region, it suffices to check only the vertex polynomials of the family. The author's main result is a sufficient condition for a given region to be a Kharitonov region.

UR - https://www.scopus.com/pages/publications/0023604322

UR - https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4049209

U2 - 10.1109/CDC.1987.272857

DO - 10.1109/CDC.1987.272857

M3 - Conference Paper

AN - SCOPUS:0023604322

VL - 1

T3 - Proceedings of the IEEE Conference on Decision and Control

SP - 440

EP - 444

BT - Proceedings of the 26th IEEE Conference on Decision and Control

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 26th IEEE Conference on Decision and Control

Y2 - 9 December 1987 through 11 December 1987

ER -

CLASS OF STABILITY REGIONS FOR WHICH A KHARITONOV LIKE THEOREM HOLDS.

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