ROBUST SCHUR POLYNOMIAL STABILITY AND KHARITONOV'S THEOREM.

F. J. Kraus; M. Mansour; B. D.O. Anderson

doi:10.1109/cdc.1987.272923

ROBUST SCHUR POLYNOMIAL STABILITY AND KHARITONOV'S THEOREM.

F. J. Kraus^*, M. Mansour, B. D.O. Anderson

^*Corresponding author for this work

Research output: Contribution to journal › Conference article › peer-review

18 Citations (Scopus)

Abstract

Robust stability properties for certain Schur polynomials are considered. By plotting coefficient variations in planes defined by variable pairs and requiring in each such plane that the region of obtained coefficients to be bounded by lines of slope 45 degree , 90 degree and 135 degree , it is shown that stability for all polynomials defined by corner points is necessary and sufficient for stability of all polynomials defined by any points in the region. Using this idea, one can construct several necessity and differing sufficiency conditions for the stability of polynomials where each coefficient can vary independently in a particular interval. As the sufficiency conditions become closer to necessity conditions, the number of distinct polynomials for which stability has to be tested increases. These results improve on V. L. Kharitonov's theorem (1979) regarding robust stabilizability.

Original language	English
Pages (from-to)	2088-2095
Number of pages	8
Journal	Proceedings of the IEEE Conference on Decision and Control
DOIs	https://doi.org/10.1109/cdc.1987.272923
Publication status	Published - 1987
Externally published	Yes

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10.1109/cdc.1987.272923

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title = "ROBUST SCHUR POLYNOMIAL STABILITY AND KHARITONOV'S THEOREM.",

abstract = "Robust stability properties for certain Schur polynomials are considered. By plotting coefficient variations in planes defined by variable pairs and requiring in each such plane that the region of obtained coefficients to be bounded by lines of slope 45 degree , 90 degree and 135 degree , it is shown that stability for all polynomials defined by corner points is necessary and sufficient for stability of all polynomials defined by any points in the region. Using this idea, one can construct several necessity and differing sufficiency conditions for the stability of polynomials where each coefficient can vary independently in a particular interval. As the sufficiency conditions become closer to necessity conditions, the number of distinct polynomials for which stability has to be tested increases. These results improve on V. L. Kharitonov's theorem (1979) regarding robust stabilizability.",

author = "Kraus, {F. J.} and M. Mansour and Anderson, {B. D.O.}",

year = "1987",

doi = "10.1109/cdc.1987.272923",

language = "English",

pages = "2088--2095",

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

issn = "0191-2216",

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

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T1 - ROBUST SCHUR POLYNOMIAL STABILITY AND KHARITONOV'S THEOREM.

AU - Kraus, F. J.

AU - Mansour, M.

AU - Anderson, B. D.O.

PY - 1987

Y1 - 1987

N2 - Robust stability properties for certain Schur polynomials are considered. By plotting coefficient variations in planes defined by variable pairs and requiring in each such plane that the region of obtained coefficients to be bounded by lines of slope 45 degree , 90 degree and 135 degree , it is shown that stability for all polynomials defined by corner points is necessary and sufficient for stability of all polynomials defined by any points in the region. Using this idea, one can construct several necessity and differing sufficiency conditions for the stability of polynomials where each coefficient can vary independently in a particular interval. As the sufficiency conditions become closer to necessity conditions, the number of distinct polynomials for which stability has to be tested increases. These results improve on V. L. Kharitonov's theorem (1979) regarding robust stabilizability.

AB - Robust stability properties for certain Schur polynomials are considered. By plotting coefficient variations in planes defined by variable pairs and requiring in each such plane that the region of obtained coefficients to be bounded by lines of slope 45 degree , 90 degree and 135 degree , it is shown that stability for all polynomials defined by corner points is necessary and sufficient for stability of all polynomials defined by any points in the region. Using this idea, one can construct several necessity and differing sufficiency conditions for the stability of polynomials where each coefficient can vary independently in a particular interval. As the sufficiency conditions become closer to necessity conditions, the number of distinct polynomials for which stability has to be tested increases. These results improve on V. L. Kharitonov's theorem (1979) regarding robust stabilizability.

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U2 - 10.1109/cdc.1987.272923

DO - 10.1109/cdc.1987.272923

M3 - Conference article

AN - SCOPUS:0023592462

SN - 0191-2216

SP - 2088

EP - 2095

JO - Proceedings of the IEEE Conference on Decision and Control

JF - Proceedings of the IEEE Conference on Decision and Control

ER -

ROBUST SCHUR POLYNOMIAL STABILITY AND KHARITONOV'S THEOREM.

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