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Routh-type table test for zero distribution of polynomials with commensurate fractional and integer degrees
Liang, Shu1; Wang, Sheng-Guo2,3,4; Wang, Yong5
2017
Source PublicationJOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
ISSN0016-0032
Volume354Issue:1Pages:83-104
AbstractThis 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.
DOI10.1016/j.jfranklin.2016.08.019
Language英语
Funding ProjectUSA NSF Grant[1115564] ; Hong Kong Branch of National Rail Transit Electrification and Automation Engineering Technology Research Center
WOS Research AreaAutomation & Control Systems ; Engineering ; Mathematics
WOS SubjectAutomation & Control Systems ; Engineering, Multidisciplinary ; Engineering, Electrical & Electronic ; Mathematics, Interdisciplinary Applications
WOS IDWOS:000392674500017
PublisherPERGAMON-ELSEVIER SCIENCE LTD
Citation statistics
Cited Times:4[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/24618
Collection中国科学院数学与系统科学研究院
Affiliation1.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
Recommended Citation
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.
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