Routh-type table test for zero distribution of polynomials with commensurate fractional and integer degrees

doi:10.1016/j.jfranklin.2016.08.019

CSpace

	Routh-type table test for zero distribution of polynomials with commensurate fractional and integer degrees
	Liang, Shu 1; Wang, Sheng-Guo 2,3,4; Wang, Yong 5
	2017
发表期刊	JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
ISSN	0016-0032
卷号	354 期号:1 页码:83-104
摘要	This paper mainly presents Routh-type table test methods for zero distribution of polynomials with commensurate fractional degrees on the left-half plane, right-half plane and imaginary axis in the complex plane. The proposed tabular methods are derived for extension and generalization of the Routh test, which is widely used in controls for zero distribution of polynomials with integer degrees. Singular cases are discussed and handled efficiently and simply. Necessary and sufficient conditions for the second singular case are completely analyzed in terms of symmetric zeros. A particular property is revealed that a polynomial with commensurate fractional degrees without pure imaginary zero may still be stable in the presence of the second singular case, which is impossible for a real polynomial with integer degrees Furthermore, we present a test to solve the zero distribution problem with respect to general sector region for polynomials with commensurate fractional degrees and real/complex coefficients. Finally, numerical examples are given to illustrate the correctness and effectiveness of the results. The proposed methods have broad application areas, including various systems, circuits and control. (C) 2016 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.
DOI	10.1016/j.jfranklin.2016.08.019
语种	英语
资助项目	USA NSF Grant[1115564] ; Hong Kong Branch of National Rail Transit Electrification and Automation Engineering Technology Research Center
WOS研究方向	Automation & Control Systems ; Engineering ; Mathematics
WOS类目	Automation & Control Systems ; Engineering, Multidisciplinary ; Engineering, Electrical & Electronic ; Mathematics, Interdisciplinary Applications
WOS记录号	WOS:000392674500017
出版者	PERGAMON-ELSEVIER SCIENCE LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/24618
专题	中国科学院数学与系统科学研究院
通讯作者	Wang, Sheng-Guo
作者单位	1.Chinese Acad Sci, Inst Syst Sci, Key Lab Syst & Control, Beijing 100190, Peoples R China 2.Univ N Carolina, Coll Engn, Charlotte, NC 28223 USA 3.Univ N Carolina, Coll Comp & Informat, Charlotte, NC 28223 USA 4.Hong Kong Polytech Univ, Dept Civil & Environm Engn, Hong Kong, Hong Kong, Peoples R China 5.USTC, Dept Automat, Hefei, Anhui, Peoples R China
推荐引用方式 GB/T 7714	Liang, Shu,Wang, Sheng-Guo,Wang, Yong. Routh-type table test for zero distribution of polynomials with commensurate fractional and integer degrees[J]. JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS,2017,354(1):83-104.
APA	Liang, Shu,Wang, Sheng-Guo,&Wang, Yong.(2017).Routh-type table test for zero distribution of polynomials with commensurate fractional and integer degrees.JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS,354(1),83-104.
MLA	Liang, Shu,et al."Routh-type table test for zero distribution of polynomials with commensurate fractional and integer degrees".JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS 354.1(2017):83-104.