{"id":"https://openalex.org/W2124057874","doi":"https://doi.org/10.1109/med.2013.6608814","title":"Notions of equivalence for linear multivariable systems","display_name":"Notions of equivalence for linear multivariable systems","publication_year":2013,"publication_date":"2013-06-01","ids":{"openalex":"https://openalex.org/W2124057874","doi":"https://doi.org/10.1109/med.2013.6608814","mag":"2124057874"},"language":"en","primary_location":{"id":"doi:10.1109/med.2013.6608814","is_oa":false,"landing_page_url":"https://doi.org/10.1109/med.2013.6608814","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"21st Mediterranean Conference on Control and Automation","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5071647997","display_name":"A.I.G. Vardulakis","orcid":"https://orcid.org/0000-0003-1200-1898"},"institutions":[{"id":"https://openalex.org/I21370196","display_name":"Aristotle University of Thessaloniki","ror":"https://ror.org/02j61yw88","country_code":"GR","type":"education","lineage":["https://openalex.org/I21370196"]}],"countries":["GR"],"is_corresponding":true,"raw_author_name":"A. I. G. Vardulakis","raw_affiliation_strings":["Department of Mathematics, Aristotle Univeristy of Thessaloniki, Thessaloniki, Greece","Dept. of Math., Aristotle Univ. of Thessaloniki, Thessaloniki, Greece"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Aristotle Univeristy of Thessaloniki, Thessaloniki, Greece","institution_ids":["https://openalex.org/I21370196"]},{"raw_affiliation_string":"Dept. of Math., Aristotle Univ. of Thessaloniki, Thessaloniki, Greece","institution_ids":["https://openalex.org/I21370196"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066594965","display_name":"Nicholas P. Karampetakis","orcid":"https://orcid.org/0000-0002-4578-5521"},"institutions":[{"id":"https://openalex.org/I21370196","display_name":"Aristotle University of Thessaloniki","ror":"https://ror.org/02j61yw88","country_code":"GR","type":"education","lineage":["https://openalex.org/I21370196"]}],"countries":["GR"],"is_corresponding":false,"raw_author_name":"N. Karampetakis","raw_affiliation_strings":["Department of Mathematics, Aristotle Univeristy of Thessaloniki, Thessaloniki, Greece","Dept. of Math., Aristotle Univ. of Thessaloniki, Thessaloniki, Greece"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Aristotle Univeristy of Thessaloniki, Thessaloniki, Greece","institution_ids":["https://openalex.org/I21370196"]},{"raw_affiliation_string":"Dept. of Math., Aristotle Univ. of Thessaloniki, Thessaloniki, Greece","institution_ids":["https://openalex.org/I21370196"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5082819385","display_name":"Efstathios Antoniou","orcid":"https://orcid.org/0000-0001-6177-6169"},"institutions":[{"id":"https://openalex.org/I77990126","display_name":"Alexander Technological Educational Institute of Thessaloniki","ror":"https://ror.org/04h36ea57","country_code":"GR","type":"education","lineage":["https://openalex.org/I77990126"]}],"countries":["GR"],"is_corresponding":false,"raw_author_name":"E. Antoniou","raw_affiliation_strings":["Department of Sciences, Alexander Technological Educational Insitute of Thessaloniki, Thessaloniki, Greece","Dept. of Sci., Alexander Technol. Educ. Insitute of Thessaloniki, Thessaloniki, Greece"],"affiliations":[{"raw_affiliation_string":"Department of Sciences, Alexander Technological Educational Insitute of Thessaloniki, Thessaloniki, Greece","institution_ids":["https://openalex.org/I77990126"]},{"raw_affiliation_string":"Dept. of Sci., Alexander Technol. Educ. Insitute of Thessaloniki, Thessaloniki, Greece","institution_ids":["https://openalex.org/I77990126"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5039053440","display_name":"Stavros Vologiannidis","orcid":"https://orcid.org/0000-0003-2945-0841"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"S. Vologiannidis","raw_affiliation_strings":["DataScouting Unlimited, Thessaloniki, Greece"],"affiliations":[{"raw_affiliation_string":"DataScouting Unlimited, Thessaloniki, Greece","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5071647997"],"corresponding_institution_ids":["https://openalex.org/I21370196"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.17641419,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"2","issue":null,"first_page":"794","last_page":"800"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.9958999752998352,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.9958999752998352,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9882000088691711,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9819999933242798,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/multivariable-calculus","display_name":"Multivariable calculus","score":0.80804044008255},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.697232186794281},{"id":"https://openalex.org/keywords/perspective","display_name":"Perspective (graphical)","score":0.6344964504241943},{"id":"https://openalex.org/keywords/variety","display_name":"Variety (cybernetics)","score":0.5826209187507629},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5083417296409607},{"id":"https://openalex.org/keywords/spectral-properties","display_name":"Spectral properties","score":0.5080506801605225},{"id":"https://openalex.org/keywords/polynomial-matrix","display_name":"Polynomial matrix","score":0.4971466362476349},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.4879538416862488},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4818640649318695},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4704025387763977},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4463120698928833},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.378055602312088},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3649616539478302},{"id":"https://openalex.org/keywords/matrix-polynomial","display_name":"Matrix polynomial","score":0.23334789276123047},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08860579133033752},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.07787081599235535},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.0685717761516571}],"concepts":[{"id":"https://openalex.org/C117312493","wikidata":"https://www.wikidata.org/wiki/Q2035437","display_name":"Multivariable calculus","level":2,"score":0.80804044008255},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.697232186794281},{"id":"https://openalex.org/C12713177","wikidata":"https://www.wikidata.org/wiki/Q1900281","display_name":"Perspective (graphical)","level":2,"score":0.6344964504241943},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.5826209187507629},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5083417296409607},{"id":"https://openalex.org/C2985906921","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Spectral properties","level":2,"score":0.5080506801605225},{"id":"https://openalex.org/C126352355","wikidata":"https://www.wikidata.org/wiki/Q2562273","display_name":"Polynomial matrix","level":4,"score":0.4971466362476349},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.4879538416862488},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4818640649318695},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4704025387763977},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4463120698928833},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.378055602312088},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3649616539478302},{"id":"https://openalex.org/C101044782","wikidata":"https://www.wikidata.org/wiki/Q6787887","display_name":"Matrix polynomial","level":3,"score":0.23334789276123047},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08860579133033752},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.07787081599235535},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0685717761516571},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C147597530","wikidata":"https://www.wikidata.org/wiki/Q369472","display_name":"Computational chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C133731056","wikidata":"https://www.wikidata.org/wiki/Q4917288","display_name":"Control engineering","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/med.2013.6608814","is_oa":false,"landing_page_url":"https://doi.org/10.1109/med.2013.6608814","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"21st Mediterranean Conference on Control and Automation","raw_type":"proceedings-article"},{"id":"pmh:oai:195.251.240.254:10184/9100","is_oa":false,"landing_page_url":"http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=6608814&url=http%3A%2F%2Fieeexplore.ieee.org%2Fxpls%2Fabs_all.jsp%3Farnumber%3D6608814","pdf_url":null,"source":{"id":"https://openalex.org/S4306401621","display_name":"Eureka! Institutional Repository (Eureka!)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210148378","host_organization_name":"Eureka Scientific","host_organization_lineage":["https://openalex.org/I4210148378"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=6589043","raw_type":"Conference article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W16781508","https://openalex.org/W430666788","https://openalex.org/W1480143973","https://openalex.org/W1594851591","https://openalex.org/W1607532558","https://openalex.org/W1977164729","https://openalex.org/W1985944188","https://openalex.org/W2005883575","https://openalex.org/W2005986740","https://openalex.org/W2010647489","https://openalex.org/W2015847333","https://openalex.org/W2015887728","https://openalex.org/W2023976076","https://openalex.org/W2031607467","https://openalex.org/W2041926662","https://openalex.org/W2059539623","https://openalex.org/W2067805107","https://openalex.org/W2078839767","https://openalex.org/W2085849252","https://openalex.org/W2102008258","https://openalex.org/W2103409198","https://openalex.org/W2110759274","https://openalex.org/W2120794985","https://openalex.org/W2127840681","https://openalex.org/W2128978199","https://openalex.org/W2129990064","https://openalex.org/W2140557463","https://openalex.org/W2141622234","https://openalex.org/W2148194793","https://openalex.org/W2161246948","https://openalex.org/W2167570714","https://openalex.org/W2175904276","https://openalex.org/W2321558489","https://openalex.org/W2406334773","https://openalex.org/W2489884345","https://openalex.org/W4213231302","https://openalex.org/W4234867792","https://openalex.org/W4245591726","https://openalex.org/W6636261327","https://openalex.org/W6722836916"],"related_works":["https://openalex.org/W1576377477","https://openalex.org/W2224575301","https://openalex.org/W2721687755","https://openalex.org/W2388146630","https://openalex.org/W418212511","https://openalex.org/W2086932047","https://openalex.org/W2099048101","https://openalex.org/W1964208669","https://openalex.org/W2112363989","https://openalex.org/W4230049560"],"abstract_inverted_index":{"The":[0],"present":[1],"paper":[2],"is":[3,87],"a":[4,13,25,38,47],"survey":[5],"on":[6],"linear":[7,75],"multivariable":[8],"systems":[9],"equivalences.":[10],"We":[11],"attempt":[12],"review":[14],"of":[15,20,33,42,49,51,62,70,72,80],"the":[16,44,57,73,81],"most":[17],"significant":[18],"types":[19,32,61,69],"system":[21,39],"equivalence":[22],"having":[23],"as":[24],"starting":[26],"point":[27,41],"matrix":[28,53],"transformations":[29],"preserving":[30],"certain":[31],"their":[34,85],"spectral":[35,63],"structure.":[36],"From":[37],"theoretic":[40],"view,":[43],"need":[45],"for":[46],"variety":[48],"forms":[50],"polynomial":[52],"equivalences,":[54],"arises":[55],"from":[56],"fact":[58],"that":[59],"different":[60,68],"invariants":[64],"give":[65],"rise":[66],"to":[67],"dynamics":[71],"underlying":[74],"system.":[76],"A":[77],"historical":[78],"perspective":[79],"key":[82],"results":[83],"and":[84],"contributors":[86],"also":[88],"given.":[89]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}