{"id":"https://openalex.org/W2161913224","doi":"https://doi.org/10.1109/cdc.2008.4738701","title":"Floquet transformations for discrete-time systems: Equivalence between periodic systems and time-invariant ones","display_name":"Floquet transformations for discrete-time systems: Equivalence between periodic systems and time-invariant ones","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W2161913224","doi":"https://doi.org/10.1109/cdc.2008.4738701","mag":"2161913224"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2008.4738701","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2008.4738701","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2008 47th IEEE Conference on Decision and Control","raw_type":"proceedings-article"},"type":"conference-paper","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://nagoya.repo.nii.ac.jp/record/10305/files/0295.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5110501389","display_name":"Yoshikazu Hayakawa","orcid":null},"institutions":[{"id":"https://openalex.org/I60134161","display_name":"Nagoya University","ror":"https://ror.org/04chrp450","country_code":"JP","type":"education","lineage":["https://openalex.org/I60134161"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Yoshikazu Hayakawa","raw_affiliation_strings":["Department of Mechanical Science and Engineering, University of Nagoya, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical Science and Engineering, University of Nagoya, Japan","institution_ids":["https://openalex.org/I60134161"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5066055821","display_name":"T. Jimbo","orcid":"https://orcid.org/0000-0001-6863-4868"},"institutions":[{"id":"https://openalex.org/I4210165351","display_name":"Toyota Central Research and Development Laboratories (Japan)","ror":"https://ror.org/05mjgqe69","country_code":"JP","type":"company","lineage":["https://openalex.org/I4210125472","https://openalex.org/I4210165351"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Tomohiko Jimbo","raw_affiliation_strings":["Toyota Central Research and Development Laboratories, Inc., Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Toyota Central Research and Development Laboratories, Inc., Japan","institution_ids":["https://openalex.org/I4210165351"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.8566,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.71537926,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"5140","last_page":"5145"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9987000226974487,"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"}},"topics":[{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9987000226974487,"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"}},{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9958999752998352,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9934999942779541,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/floquet-theory","display_name":"Floquet theory","score":0.9738954305648804},{"id":"https://openalex.org/keywords/invertible-matrix","display_name":"Invertible matrix","score":0.7895679473876953},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6419435739517212},{"id":"https://openalex.org/keywords/discrete-time-and-continuous-time","display_name":"Discrete time and continuous time","score":0.5578187108039856},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.5053609013557434},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.4865983724594116},{"id":"https://openalex.org/keywords/matrix-similarity","display_name":"Matrix similarity","score":0.4481489062309265},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.4420904815196991},{"id":"https://openalex.org/keywords/lti-system-theory","display_name":"LTI system theory","score":0.4199027717113495},{"id":"https://openalex.org/keywords/transformation-matrix","display_name":"Transformation matrix","score":0.4174094796180725},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3832131624221802},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.35118567943573},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.13389867544174194},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1111392080783844},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.1107785701751709},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.07874119281768799}],"concepts":[{"id":"https://openalex.org/C55649039","wikidata":"https://www.wikidata.org/wiki/Q902618","display_name":"Floquet theory","level":3,"score":0.9738954305648804},{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.7895679473876953},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6419435739517212},{"id":"https://openalex.org/C55689738","wikidata":"https://www.wikidata.org/wiki/Q15963867","display_name":"Discrete time and continuous time","level":2,"score":0.5578187108039856},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5053609013557434},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.4865983724594116},{"id":"https://openalex.org/C39739852","wikidata":"https://www.wikidata.org/wiki/Q254491","display_name":"Matrix similarity","level":3,"score":0.4481489062309265},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.4420904815196991},{"id":"https://openalex.org/C87698059","wikidata":"https://www.wikidata.org/wiki/Q1808960","display_name":"LTI system theory","level":3,"score":0.4199027717113495},{"id":"https://openalex.org/C165443888","wikidata":"https://www.wikidata.org/wiki/Q1482183","display_name":"Transformation matrix","level":3,"score":0.4174094796180725},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3832131624221802},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.35118567943573},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.13389867544174194},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1111392080783844},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.1107785701751709},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.07874119281768799},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C39920418","wikidata":"https://www.wikidata.org/wiki/Q11476","display_name":"Kinematics","level":2,"score":0.0},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/cdc.2008.4738701","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2008.4738701","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2008 47th IEEE Conference on Decision and Control","raw_type":"proceedings-article"},{"id":"pmh:oai:irdb.nii.ac.jp:01152:0001453452","is_oa":true,"landing_page_url":"https://nagoya.repo.nii.ac.jp/records/10305","pdf_url":"https://nagoya.repo.nii.ac.jp/record/10305/files/0295.pdf","source":{"id":"https://openalex.org/S7407056385","display_name":"Institutional Repositories DataBase (IRDB)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I184597095","host_organization_name":"National Institute of Informatics","host_organization_lineage":["https://openalex.org/I184597095"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"47th IEEE Conference on Decision and Control (CDC 2008)","raw_type":"journal article"}],"best_oa_location":{"id":"pmh:oai:irdb.nii.ac.jp:01152:0001453452","is_oa":true,"landing_page_url":"https://nagoya.repo.nii.ac.jp/records/10305","pdf_url":"https://nagoya.repo.nii.ac.jp/record/10305/files/0295.pdf","source":{"id":"https://openalex.org/S7407056385","display_name":"Institutional Repositories DataBase (IRDB)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I184597095","host_organization_name":"National Institute of Informatics","host_organization_lineage":["https://openalex.org/I184597095"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"47th IEEE Conference on Decision and Control (CDC 2008)","raw_type":"journal article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2161913224.pdf","grobid_xml":"https://content.openalex.org/works/W2161913224.grobid-xml"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W83533993","https://openalex.org/W641468332","https://openalex.org/W1488435683","https://openalex.org/W1518553437","https://openalex.org/W1534096605","https://openalex.org/W1971614731","https://openalex.org/W2015373818","https://openalex.org/W2028170488","https://openalex.org/W2091536355","https://openalex.org/W2111828158","https://openalex.org/W2128978199","https://openalex.org/W2130613450","https://openalex.org/W2143447059","https://openalex.org/W2152366256","https://openalex.org/W2161719008","https://openalex.org/W6620850251","https://openalex.org/W6632138476"],"related_works":["https://openalex.org/W4386631510","https://openalex.org/W2425100171","https://openalex.org/W2143134818","https://openalex.org/W2004799165","https://openalex.org/W1975902360","https://openalex.org/W1978034477","https://openalex.org/W1899050863","https://openalex.org/W2387658382","https://openalex.org/W2080533896","https://openalex.org/W2125180553"],"abstract_inverted_index":{"This":[0],"paper":[1,71],"considers":[2],"discrete-time":[3,36],"periodic":[4,14],"linear":[5],"systems":[6,15,100],"and":[7,57,69],"their":[8],"Floquet":[9,37,61,85,96],"transformations,":[10],"by":[11,78],"which":[12,79],"the":[13,24,35,41,46,52,81],"can":[16],"be":[17,88],"equivalently":[18],"transformed":[19],"to":[20,33,63,73,98],"time-invariant":[21],"ones.":[22],"When":[23],"system":[25,42],"matrix":[26,43],"is":[27,30,44,48,101],"nonsingular,":[28],"it":[29],"very":[31],"easy":[32],"derive":[34],"transformation,":[38],"however,":[39],"when":[40],"singular,":[45],"derivation":[47],"essentially":[49],"different":[50],"from":[51],"continuous-time":[53],"case.":[54],"A":[55],"necessary":[56],"sufficient":[58],"condition":[59],"for":[60],"transformation":[62],"exist":[64],"has":[65],"been":[66],"already":[67],"known":[68],"this":[70],"aims":[72],"give":[74],"a":[75],"simpler":[76],"proof,":[77],"all":[80],"similarity":[82],"classes":[83],"of":[84,95],"transformations":[86,97],"could":[87],"made":[89],"clear.":[90],"And":[91],"also":[92],"an":[93],"extension":[94],"non-autonomous":[99],"shown.":[102]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2016,"cited_by_count":2}],"updated_date":"2026-08-18T07:49:30.821534","created_date":"2025-10-10T00:00:00"}
