{"id":"https://openalex.org/W2079815221","doi":"https://doi.org/10.1109/cdc.2011.6160552","title":"State space representation of SISO periodic behaviors","display_name":"State space representation of SISO periodic behaviors","publication_year":2011,"publication_date":"2011-12-01","ids":{"openalex":"https://openalex.org/W2079815221","doi":"https://doi.org/10.1109/cdc.2011.6160552","mag":"2079815221"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2011.6160552","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2011.6160552","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Conference on Decision and Control and European Control Conference","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/A5036259619","display_name":"Jos\u00e9 Carlos Brandi Aleixo","orcid":"https://orcid.org/0000-0002-8244-7978"},"institutions":[{"id":"https://openalex.org/I161321875","display_name":"University of Beira Interior","ror":"https://ror.org/03nf36p02","country_code":"PT","type":"education","lineage":["https://openalex.org/I161321875"]}],"countries":["PT"],"is_corresponding":true,"raw_author_name":"Jose C. Aleixo","raw_affiliation_strings":["Department of Mathematics, University of Beira Interior, Covilhaa, Portugal","Department of Mathematics, University of Beira Interior, 6201-001 Covilh\u00e3, Portugal"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Beira Interior, Covilhaa, Portugal","institution_ids":["https://openalex.org/I161321875"]},{"raw_affiliation_string":"Department of Mathematics, University of Beira Interior, 6201-001 Covilh\u00e3, Portugal","institution_ids":["https://openalex.org/I161321875"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028177375","display_name":"Paula Rocha","orcid":"https://orcid.org/0000-0001-5037-3372"},"institutions":[{"id":"https://openalex.org/I182534213","display_name":"Universidade do Porto","ror":"https://ror.org/043pwc612","country_code":"PT","type":"education","lineage":["https://openalex.org/I182534213"]}],"countries":["PT"],"is_corresponding":false,"raw_author_name":"Paula Rocha","raw_affiliation_strings":["Faculty of Engineering, University of Oporto, Porto, Portugal","Faculty of Engineering, University of Oporto, 4200-465 Porto, Portugal"],"affiliations":[{"raw_affiliation_string":"Faculty of Engineering, University of Oporto, Porto, Portugal","institution_ids":["https://openalex.org/I182534213"]},{"raw_affiliation_string":"Faculty of Engineering, University of Oporto, 4200-465 Porto, Portugal","institution_ids":["https://openalex.org/I182534213"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5009595862","display_name":"Jan C. Willems","orcid":null},"institutions":[{"id":"https://openalex.org/I99464096","display_name":"KU Leuven","ror":"https://ror.org/05f950310","country_code":"BE","type":"education","lineage":["https://openalex.org/I99464096"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Jan C. Willems","raw_affiliation_strings":["ESAT, SCD (SISTA), KU Leuven, Heverlee, Belgium","ESAT/SCD (SISTA), K.U.Leuven, B-3001 Heverlee, Belgium"],"affiliations":[{"raw_affiliation_string":"ESAT, SCD (SISTA), KU Leuven, Heverlee, Belgium","institution_ids":["https://openalex.org/I99464096"]},{"raw_affiliation_string":"ESAT/SCD (SISTA), K.U.Leuven, B-3001 Heverlee, Belgium","institution_ids":["https://openalex.org/I99464096"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5036259619"],"corresponding_institution_ids":["https://openalex.org/I161321875"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.1225908,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"14","issue":null,"first_page":"1545","last_page":"1550"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11236","display_name":"Control Systems and Identification","score":0.9988999962806702,"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/T11236","display_name":"Control Systems and Identification","score":0.9988999962806702,"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/T10876","display_name":"Fault Detection and Control Systems","score":0.9970999956130981,"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/T10791","display_name":"Advanced Control Systems Optimization","score":0.9955000281333923,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/transfer-function","display_name":"Transfer function","score":0.6729198694229126},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.6595720052719116},{"id":"https://openalex.org/keywords/state-space","display_name":"State space","score":0.6254197955131531},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.6001638770103455},{"id":"https://openalex.org/keywords/state-space-representation","display_name":"State-space representation","score":0.5380005836486816},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.5103582739830017},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.48902401328086853},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.48242005705833435},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4780716896057129},{"id":"https://openalex.org/keywords/periodic-function","display_name":"Periodic function","score":0.43464431166648865},{"id":"https://openalex.org/keywords/lti-system-theory","display_name":"LTI system theory","score":0.4335617423057556},{"id":"https://openalex.org/keywords/periodic-sequence","display_name":"Periodic sequence","score":0.42245718836784363},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.41094741225242615},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3755279779434204},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.36903858184814453},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.34145963191986084},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1833801567554474},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.12371155619621277},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.10790249705314636},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.060749202966690063}],"concepts":[{"id":"https://openalex.org/C81299745","wikidata":"https://www.wikidata.org/wiki/Q334269","display_name":"Transfer function","level":2,"score":0.6729198694229126},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.6595720052719116},{"id":"https://openalex.org/C72434380","wikidata":"https://www.wikidata.org/wiki/Q230930","display_name":"State space","level":2,"score":0.6254197955131531},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.6001638770103455},{"id":"https://openalex.org/C52918065","wikidata":"https://www.wikidata.org/wiki/Q230945","display_name":"State-space representation","level":2,"score":0.5380005836486816},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5103582739830017},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.48902401328086853},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.48242005705833435},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4780716896057129},{"id":"https://openalex.org/C98644592","wikidata":"https://www.wikidata.org/wiki/Q184743","display_name":"Periodic function","level":2,"score":0.43464431166648865},{"id":"https://openalex.org/C87698059","wikidata":"https://www.wikidata.org/wiki/Q1808960","display_name":"LTI system theory","level":3,"score":0.4335617423057556},{"id":"https://openalex.org/C120241303","wikidata":"https://www.wikidata.org/wiki/Q3503302","display_name":"Periodic sequence","level":2,"score":0.42245718836784363},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.41094741225242615},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3755279779434204},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.36903858184814453},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.34145963191986084},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1833801567554474},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.12371155619621277},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.10790249705314636},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.060749202966690063},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","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},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cdc.2011.6160552","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2011.6160552","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Conference on Decision and Control and European Control Conference","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W63990713","https://openalex.org/W99995160","https://openalex.org/W1528718180","https://openalex.org/W1535144613","https://openalex.org/W1994147271","https://openalex.org/W2015841828","https://openalex.org/W2019653255","https://openalex.org/W2047215894","https://openalex.org/W2054116729","https://openalex.org/W2055380033","https://openalex.org/W2062880439","https://openalex.org/W2074986619","https://openalex.org/W2086703735","https://openalex.org/W2105587146","https://openalex.org/W2146560209","https://openalex.org/W2148443868","https://openalex.org/W2150129308","https://openalex.org/W2594477128","https://openalex.org/W6632015301","https://openalex.org/W6734166327"],"related_works":["https://openalex.org/W2579634771","https://openalex.org/W2385169700","https://openalex.org/W2356502513","https://openalex.org/W4388320481","https://openalex.org/W3013517953","https://openalex.org/W1560664277","https://openalex.org/W2756401664","https://openalex.org/W2060682274","https://openalex.org/W2338837772","https://openalex.org/W2083232669"],"abstract_inverted_index":{"The":[0],"aim":[1],"of":[2],"this":[3],"paper":[4],"is":[5],"to":[6,23,28],"obtain":[7],"periodic":[8,13,30],"state":[9],"space":[10],"representations":[11],"for":[12],"input-output":[14],"behavioral":[15],"systems":[16],"using":[17],"a":[18,25,29,45],"lifting":[19],"technique":[20],"which":[21],"allows":[22],"associate":[24],"time-invariant":[26],"behavior":[27],"one.":[31],"Our":[32],"approach":[33],"differs":[34],"from":[35,44,51],"the":[36],"classical":[37],"one":[38],"since":[39],"we":[40],"do":[41],"not":[42],"start":[43],"transfer":[46],"function":[47],"description":[48],"but":[49],"rather":[50],"linear":[52],"difference":[53],"equations":[54],"with":[55],"periodically":[56],"time-varying":[57],"coefficients.":[58]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
