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

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

Research output: Chapter in Book/Report/Conference proceedingConference 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 languageEnglish
Title of host publicationProceedings of the 1998 American Control Conference, ACC 1998
Pages3206-3209
Number of pages4
DOIs
Publication statusPublished - 1998 Dec 1
Event1998 American Control Conference, ACC 1998 - Philadelphia, PA, United States
Duration: 1998 Jun 241998 Jun 26

Publication series

NameProceedings of the American Control Conference
Volume5
ISSN (Print)0743-1619

Other

Other1998 American Control Conference, ACC 1998
CountryUnited States
CityPhiladelphia, PA
Period98-06-2498-06-26

All Science Journal Classification (ASJC) codes

  • Electrical and Electronic Engineering

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    Ho, M. T., Datta, A., & Bhattacharyya, S. P. (1998). An extension of the generalized hermite-biehler theorem: Relaxation of earlier assumptions. In Proceedings of the 1998 American Control Conference, ACC 1998 (pp. 3206-3209). [688454] (Proceedings of the American Control Conference; Vol. 5). https://doi.org/10.1109/ACC.1998.688454