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A novel frequency-domain approach for the exact range of imaginary spectra and the stability analysis of LTI systems with two delays

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dc.title A novel frequency-domain approach for the exact range of imaginary spectra and the stability analysis of LTI systems with two delays en
dc.contributor.author Yuan, Chengzhi
dc.contributor.author Song, Shuang
dc.contributor.author Gao, Qinbin
dc.contributor.author Karimi, Hamid Reza
dc.contributor.author Pekař, Libor
dc.contributor.author Guo, Shenghui
dc.relation.ispartof IEEE Access
dc.identifier.issn 2169-3536 Scopus Sources, Sherpa/RoMEO, JCR
dc.date.issued 2020
utb.relation.volume 8
dc.citation.spage 36595
dc.citation.epage 36601
dc.type article
dc.language.iso en
dc.publisher Institute of Electrical and Electronics Engineers Inc.
dc.identifier.doi 10.1109/ACCESS.2020.2973834
dc.relation.uri https://ieeexplore.ieee.org/document/9000594
dc.subject Dixon resultant en
dc.subject frequency domain en
dc.subject stability en
dc.subject Time-delay system en
dc.description.abstract This paper presents a novel frequency-domain approach to reveal the exact range of the imaginary spectra and the stability of linear time-invariant systems with two delays. First, an exact relation, i.e., the Rekasius substitution, is used to replace the exponential term caused by the delays in order to transform the transcendental characteristic equation to a quasi-polynomial. Second, this quasi-polynomial is uniquely tackled by our proposed Dixon resultant and discriminant theory, leading to the elimination of delay-related elements and the revelation of the exact range of the frequency spectra of the original system of interest. Then, by sweeping the frequency over this obtained range, the stability switching curves are declared exhaustively. Last, we deploy the cluster treatment of characteristic roots (CTCR) paradigm to reveal the exact and complete stability map. The proposed methodologies are tested and verified by a numerical method called Quasi-Polynomial mapping-based Root finder (QPmR) over an example case. © 2013 IEEE. en
utb.faculty Faculty of Applied Informatics
dc.identifier.uri http://hdl.handle.net/10563/1009625
utb.identifier.obdid 43881284
utb.identifier.scopus 2-s2.0-85081136503
utb.identifier.wok 000524616200004
utb.source j-scopus
dc.date.accessioned 2020-03-26T10:44:55Z
dc.date.available 2020-03-26T10:44:55Z
dc.rights Attribution 3.0 Unported
dc.rights.uri https://creativecommons.org/licenses/by/3.0/
dc.rights.access openAccess
utb.contributor.internalauthor Pekař, Libor
utb.wos.affiliation [Yuan, Chengzhi] Univ Rhode Isl, Dept Mech Ind & Syst Engn, Kingston, RI 02881 USA; [Song, Shuang; Gao, Qingbin] Harbin Inst Technol Shenzhen, Sch Mech Engn & Automat, Shenzhen 518055, Peoples R China; [Karimi, Hamid Reza] Politecn Milan, Mech Engn Dept, I-20156 Milan, Italy; [Pekar, Libor] Tomas Bata Univ Zlin, Appl Informat Dept, Zlin 76005, Czech Republic; [Guo, Shenghui] Suzhou Univ Sci & Technol, Coll Elect & Informat Engn, Suzhou 215009, Peoples R China
utb.scopus.affiliation Department of Mechanical, Industrial and Systems Engineering, University of Rhode Island, Kingston, RI 02881, United States; School of Mechanical Engineering and Automation, Harbin Institute of Technology (Shenzhen), Shenzhen, 518055, China; Mechanical Engineering Department, Politecnico di Milano, Milan, 20156, Italy; Applied Informatics Department, Tomas Bata University in Zlin, Zlin, 760 05, Czech Republic; College of Electronics and Information Engineering, Suzhou University of Science and Technology, Suzhou, 215009, China
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Attribution 3.0 Unported Except where otherwise noted, this item's license is described as Attribution 3.0 Unported