Basis Functions for a Transient Analysis of Linear Commensurate Fractional-Order Systems

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dc.contributor.authorBiolek, Daliborcs
dc.contributor.authorBiolková, Vieracs
dc.contributor.authorKolka, Zdeněkcs
dc.contributor.authorBiolek, Zdeněkcs
dc.coverage.issue7cs
dc.coverage.volume16cs
dc.date.issued2023-07-13cs
dc.description.abstractIn this paper, the possibilities of expressing the natural response of a linear commensurate fractional-order system (FOS) as a linear combination of basis functions are analyzed. For all possible types of s(& alpha;)-domain poles, the corresponding basis functions are found, the kernel of which is the two-parameter Mittag-Leffler function E-& alpha;(,& beta;), & beta; = & alpha;. It is pointed out that there are mutually unambiguous correspondences between the basis functions of FOS and the known basis functions of the integer-order system (IOS) for & alpha; = 1. This correspondence can be used to algorithmically find analytical formulas for the impulse responses of FOS when the formulas for the characteristics of IOS are known. It is shown that all basis functions of FOS can be generated with Podlubny's function of type & epsilon;(k) (t, c; & alpha;, & alpha;), where c and k are the corresponding pole and its multiplicity, respectively.en
dc.formattextcs
dc.format.extent1-22cs
dc.format.mimetypeapplication/pdfcs
dc.identifier.citationAlgorithms. 2023, vol. 16, issue 7, p. 1-22.en
dc.identifier.doi10.3390/a16070335cs
dc.identifier.issn1999-4893cs
dc.identifier.orcid0000-0002-7607-6146cs
dc.identifier.orcid0000-0003-2589-2722cs
dc.identifier.orcid0000-0002-7034-9430cs
dc.identifier.other184376cs
dc.identifier.researcheridE-4125-2018cs
dc.identifier.researcheridE-3698-2018cs
dc.identifier.researcheridE-3657-2018cs
dc.identifier.scopus6603672687cs
dc.identifier.scopus6506028849cs
dc.identifier.scopus6602443208cs
dc.identifier.urihttp://hdl.handle.net/11012/244995
dc.language.isoencs
dc.publisherMDPIcs
dc.relation.ispartofAlgorithmscs
dc.relation.urihttps://www.mdpi.com/1999-4893/16/7/335cs
dc.rightsCreative Commons Attribution 4.0 Internationalcs
dc.rights.accessopenAccesscs
dc.rights.sherpahttp://www.sherpa.ac.uk/romeo/issn/1999-4893/cs
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/cs
dc.subjectMittag-Leffler functionen
dc.subjectcommensurate fractional-order systemen
dc.subjectbasis functionen
dc.subjectimpulse responseen
dc.titleBasis Functions for a Transient Analysis of Linear Commensurate Fractional-Order Systemsen
dc.type.driverarticleen
dc.type.statusPeer-revieweden
dc.type.versionpublishedVersionen
sync.item.dbidVAV-184376en
sync.item.dbtypeVAVen
sync.item.insts2025.02.03 15:41:16en
sync.item.modts2025.01.17 18:43:37en
thesis.grantorVysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií. Ústav radioelektronikycs
thesis.grantorVysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií. Ústav mikroelektronikycs
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