An extension of the generalized hermite-biehler theorem: Relaxation of earlier assumptions

Ming Tzu Ho; Aniruddha Datta; S. P. Bhattacharyya

doi:10.1109/ACC.1998.688454

An extension of the generalized hermite-biehler theorem: Relaxation of earlier assumptions

Ming Tzu Ho, Aniruddha Datta, S. P. Bhattacharyya

Department of Engineering Science

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

4 Citations (Scopus)

Abstract

Recently in [1, 3], a generalization of the classical Hermite-Biehler Theorem was derived and shown to be useful for solving a number of fixed order and structure stabilization problems. This generalization, though adequate for solving these stabilization problems, required the assumption that the polynomial in question have no roots on the imaginary axis except for possibly a simple root at the origin. In this note, the result of [1] is extended to also allow roots on the imaginary axis: the main conclusion is that the roots, if any, at the origin modify the earlier Theorem statement only very slightly while the other imaginary axis roots leave it unchanged. The extension presented here permits a clearer exposition of the stabilization results in [1, 3].

Original language	English
Title of host publication	Proceedings of the 1998 American Control Conference, ACC 1998
Pages	3206-3209
Number of pages	4
DOIs	https://doi.org/10.1109/ACC.1998.688454
Publication status	Published - 1998
Event	1998 American Control Conference, ACC 1998 - Philadelphia, PA, United States Duration: 1998 Jun 24 → 1998 Jun 26

Publication series

Name	Proceedings of the American Control Conference
Volume	5
ISSN (Print)	0743-1619

Other

Other	1998 American Control Conference, ACC 1998
Country/Territory	United States
City	Philadelphia, PA
Period	98-06-24 → 98-06-26

All Science Journal Classification (ASJC) codes

Electrical and Electronic Engineering

Access to Document

10.1109/ACC.1998.688454

Cite this

@inproceedings{9ffdcfdfd44c40e78eb980fa9a2ab5d9,

title = "An extension of the generalized hermite-biehler theorem: Relaxation of earlier assumptions",

abstract = "Recently in [1, 3], a generalization of the classical Hermite-Biehler Theorem was derived and shown to be useful for solving a number of fixed order and structure stabilization problems. This generalization, though adequate for solving these stabilization problems, required the assumption that the polynomial in question have no roots on the imaginary axis except for possibly a simple root at the origin. In this note, the result of [1] is extended to also allow roots on the imaginary axis: the main conclusion is that the roots, if any, at the origin modify the earlier Theorem statement only very slightly while the other imaginary axis roots leave it unchanged. The extension presented here permits a clearer exposition of the stabilization results in [1, 3].",

author = "Ho, {Ming Tzu} and Aniruddha Datta and Bhattacharyya, {S. P.}",

year = "1998",

doi = "10.1109/ACC.1998.688454",

language = "English",

isbn = "0780345304",

series = "Proceedings of the American Control Conference",

pages = "3206--3209",

booktitle = "Proceedings of the 1998 American Control Conference, ACC 1998",

note = "1998 American Control Conference, ACC 1998 ; Conference date: 24-06-1998 Through 26-06-1998",

}

Ho, MT, Datta, A & Bhattacharyya, SP 1998, An extension of the generalized hermite-biehler theorem: Relaxation of earlier assumptions. in Proceedings of the 1998 American Control Conference, ACC 1998., 688454, Proceedings of the American Control Conference, vol. 5, pp. 3206-3209, 1998 American Control Conference, ACC 1998, Philadelphia, PA, United States, 98-06-24. https://doi.org/10.1109/ACC.1998.688454

An extension of the generalized hermite-biehler theorem: Relaxation of earlier assumptions. / Ho, Ming Tzu; Datta, Aniruddha; Bhattacharyya, S. P.
Proceedings of the 1998 American Control Conference, ACC 1998. 1998. p. 3206-3209 688454 (Proceedings of the American Control Conference; Vol. 5).

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

TY - GEN

T1 - An extension of the generalized hermite-biehler theorem

T2 - 1998 American Control Conference, ACC 1998

AU - Ho, Ming Tzu

AU - Datta, Aniruddha

AU - Bhattacharyya, S. P.

PY - 1998

Y1 - 1998

N2 - Recently in [1, 3], a generalization of the classical Hermite-Biehler Theorem was derived and shown to be useful for solving a number of fixed order and structure stabilization problems. This generalization, though adequate for solving these stabilization problems, required the assumption that the polynomial in question have no roots on the imaginary axis except for possibly a simple root at the origin. In this note, the result of [1] is extended to also allow roots on the imaginary axis: the main conclusion is that the roots, if any, at the origin modify the earlier Theorem statement only very slightly while the other imaginary axis roots leave it unchanged. The extension presented here permits a clearer exposition of the stabilization results in [1, 3].

AB - Recently in [1, 3], a generalization of the classical Hermite-Biehler Theorem was derived and shown to be useful for solving a number of fixed order and structure stabilization problems. This generalization, though adequate for solving these stabilization problems, required the assumption that the polynomial in question have no roots on the imaginary axis except for possibly a simple root at the origin. In this note, the result of [1] is extended to also allow roots on the imaginary axis: the main conclusion is that the roots, if any, at the origin modify the earlier Theorem statement only very slightly while the other imaginary axis roots leave it unchanged. The extension presented here permits a clearer exposition of the stabilization results in [1, 3].

UR - http://www.scopus.com/inward/record.url?scp=33645417614&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33645417614&partnerID=8YFLogxK

U2 - 10.1109/ACC.1998.688454

DO - 10.1109/ACC.1998.688454

M3 - Conference contribution

AN - SCOPUS:33645417614

SN - 0780345304

SN - 9780780345300

T3 - Proceedings of the American Control Conference

SP - 3206

EP - 3209

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

Y2 - 24 June 1998 through 26 June 1998

ER -

An extension of the generalized hermite-biehler theorem: Relaxation of earlier assumptions

Abstract

Publication series

Other

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this