Generating edges of D-stable polynomials

Adly T. Fam

Generating edges of D-stable polynomials

Adly T. Fam

Department of Electrical Engineering

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

Abstract

It is shown that if a polynomial P is D-stable, where D is convex and contains the origin, then all convex linear combinations of P and its normalized derivative, zP′/n, are also D-stable. It is also shown that convex linear combinations of the logarithmic derivatives of a D-stable polynomial with a convex D have both their pole and zeros in D. Both theorems provide an example of how to generate edges and polytopes of D-stable polynomials and rational functions from a given finite set of D-stable polynomials.

Original language	English
Pages (from-to)	2271-2272
Number of pages	2
Journal	Proceedings of the IEEE Conference on Decision and Control
Volume	3
State	Published - 1989
Event	Proceedings of the 28th IEEE Conference on Decision and Control. Part 2 (of 3) - Tampa, FL, USA Duration: Dec 13 1989 → Dec 15 1989

Cite this

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title = "Generating edges of D-stable polynomials",

abstract = "It is shown that if a polynomial P is D-stable, where D is convex and contains the origin, then all convex linear combinations of P and its normalized derivative, zP′/n, are also D-stable. It is also shown that convex linear combinations of the logarithmic derivatives of a D-stable polynomial with a convex D have both their pole and zeros in D. Both theorems provide an example of how to generate edges and polytopes of D-stable polynomials and rational functions from a given finite set of D-stable polynomials.",

author = "Fam, \{Adly T.\}",

year = "1989",

language = "English",

volume = "3",

pages = "2271--2272",

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

issn = "0743-1546",

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

note = "Proceedings of the 28th IEEE Conference on Decision and Control. Part 2 (of 3) ; Conference date: 13-12-1989 Through 15-12-1989",

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TY - JOUR

T1 - Generating edges of D-stable polynomials

AU - Fam, Adly T.

PY - 1989

Y1 - 1989

N2 - It is shown that if a polynomial P is D-stable, where D is convex and contains the origin, then all convex linear combinations of P and its normalized derivative, zP′/n, are also D-stable. It is also shown that convex linear combinations of the logarithmic derivatives of a D-stable polynomial with a convex D have both their pole and zeros in D. Both theorems provide an example of how to generate edges and polytopes of D-stable polynomials and rational functions from a given finite set of D-stable polynomials.

AB - It is shown that if a polynomial P is D-stable, where D is convex and contains the origin, then all convex linear combinations of P and its normalized derivative, zP′/n, are also D-stable. It is also shown that convex linear combinations of the logarithmic derivatives of a D-stable polynomial with a convex D have both their pole and zeros in D. Both theorems provide an example of how to generate edges and polytopes of D-stable polynomials and rational functions from a given finite set of D-stable polynomials.

UR - https://www.scopus.com/pages/publications/0024934536

M3 - Conference article

AN - SCOPUS:0024934536

SN - 0743-1546

VL - 3

SP - 2271

EP - 2272

JO - Proceedings of the IEEE Conference on Decision and Control

JF - Proceedings of the IEEE Conference on Decision and Control

T2 - Proceedings of the 28th IEEE Conference on Decision and Control. Part 2 (of 3)

Y2 - 13 December 1989 through 15 December 1989

ER -

Generating edges of D-stable polynomials

Abstract

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