A New Tabular form for Determining Root Distribution of a Complex Polynomial with Respect to the Imaginary Axis

Shyan S. Chen; Jason S.H. Tsai

doi:10.1109/9.241571

A New Tabular form for Determining Root Distribution of a Complex Polynomial with Respect to the Imaginary Axis

Shyan S. Chen
, Jason S.H. Tsai

電機工程學系

研究成果: Article › 同行評審

23 引文斯高帕斯（Scopus）

摘要

The original Routh table dealing with real polynomials is further investigated for complex polynomials. A new tabular form for determining root distribution of a complex polynomial with respect to the imaginary axis is developed, and modified procedures for directly treating singularities in the array are proposed. Also, new procedures are developed for determining the respective orders of simple and/or repeated roots lying on the imaginary axis. As a result, the situation of conditional stability or instability can be distinguished by the criteria developed in this note.

原文	English
頁（從 - 到）	1536-1541
頁數	6
期刊	IEEE Transactions on Automatic Control
卷	38
發行號	10
DOIs	https://doi.org/10.1109/9.241571
出版狀態	Published - 1993 10月

All Science Journal Classification (ASJC) codes

控制與系統工程
電腦科學應用
電氣與電子工程

存取文件

10.1109/9.241571

其它文件與鏈接

Link to publication in Scopus

引用此

@article{6026b385c64440039eb16cb036971410,

title = "A New Tabular form for Determining Root Distribution of a Complex Polynomial with Respect to the Imaginary Axis",

abstract = "The original Routh table dealing with real polynomials is further investigated for complex polynomials. A new tabular form for determining root distribution of a complex polynomial with respect to the imaginary axis is developed, and modified procedures for directly treating singularities in the array are proposed. Also, new procedures are developed for determining the respective orders of simple and/or repeated roots lying on the imaginary axis. As a result, the situation of conditional stability or instability can be distinguished by the criteria developed in this note.",

author = "Chen, \{Shyan S.\} and Tsai, \{Jason S.H.\}",

note = "Funding Information: work was supported by the National Science Council of the Republic of China under contract NSC-81-0404-E-006-516.",

year = "1993",

month = oct,

doi = "10.1109/9.241571",

language = "English",

volume = "38",

pages = "1536--1541",

journal = "IEEE Transactions on Automatic Control",

issn = "0018-9286",

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

number = "10",

}

TY - JOUR

T1 - A New Tabular form for Determining Root Distribution of a Complex Polynomial with Respect to the Imaginary Axis

AU - Chen, Shyan S.

AU - Tsai, Jason S.H.

N1 - Funding Information: work was supported by the National Science Council of the Republic of China under contract NSC-81-0404-E-006-516.

PY - 1993/10

Y1 - 1993/10

N2 - The original Routh table dealing with real polynomials is further investigated for complex polynomials. A new tabular form for determining root distribution of a complex polynomial with respect to the imaginary axis is developed, and modified procedures for directly treating singularities in the array are proposed. Also, new procedures are developed for determining the respective orders of simple and/or repeated roots lying on the imaginary axis. As a result, the situation of conditional stability or instability can be distinguished by the criteria developed in this note.

AB - The original Routh table dealing with real polynomials is further investigated for complex polynomials. A new tabular form for determining root distribution of a complex polynomial with respect to the imaginary axis is developed, and modified procedures for directly treating singularities in the array are proposed. Also, new procedures are developed for determining the respective orders of simple and/or repeated roots lying on the imaginary axis. As a result, the situation of conditional stability or instability can be distinguished by the criteria developed in this note.

UR - https://www.scopus.com/pages/publications/0027683815

UR - https://www.scopus.com/pages/publications/0027683815#tab=citedBy

U2 - 10.1109/9.241571

DO - 10.1109/9.241571

M3 - Article

AN - SCOPUS:0027683815

SN - 0018-9286

VL - 38

SP - 1536

EP - 1541

JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

IS - 10

ER -

A New Tabular form for Determining Root Distribution of a Complex Polynomial with Respect to the Imaginary Axis

摘要

All Science Journal Classification (ASJC) codes

存取文件

其它文件與鏈接

指紋

引用此