{"id":"https://openalex.org/W1984227841","doi":"https://doi.org/10.1080/00207720310001612909","title":"Discrete-time timescale analysis via a new separation ratio and unified approach","display_name":"Discrete-time timescale analysis via a new separation ratio and unified approach","publication_year":2003,"publication_date":"2003-05-01","ids":{"openalex":"https://openalex.org/W1984227841","doi":"https://doi.org/10.1080/00207720310001612909","mag":"1984227841"},"language":"en","primary_location":{"id":"doi:10.1080/00207720310001612909","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207720310001612909","pdf_url":null,"source":{"id":"https://openalex.org/S129640837","display_name":"International Journal of Systems Science","issn_l":"0020-7721","issn":["0020-7721","1464-5319"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Systems Science","raw_type":"journal-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/A5025141175","display_name":"Hardev Kaur","orcid":"https://orcid.org/0000-0001-6979-8370"},"institutions":[{"id":"https://openalex.org/I102461120","display_name":"Marquette University","ror":"https://ror.org/04gr4te78","country_code":"US","type":"education","lineage":["https://openalex.org/I102461120"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Hardev Singh","raw_affiliation_strings":["Department of Electrical and Computer Engineering , Marquette University , PO Box 1881 , Milwaukee , WI 53201-1881 , USA","Department of Electrical and Computer Engineering, Marquette University, PO Box 1881, Milwaukee, WI 53201-1881, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering , Marquette University , PO Box 1881 , Milwaukee , WI 53201-1881 , USA","institution_ids":["https://openalex.org/I102461120"]},{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Marquette University, PO Box 1881, Milwaukee, WI 53201-1881, USA","institution_ids":["https://openalex.org/I102461120"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5075761811","display_name":"R.H. Brown","orcid":null},"institutions":[{"id":"https://openalex.org/I102461120","display_name":"Marquette University","ror":"https://ror.org/04gr4te78","country_code":"US","type":"education","lineage":["https://openalex.org/I102461120"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ronald H. Brown","raw_affiliation_strings":["Department of Electrical and Computer Engineering , Marquette University , PO Box 1881 , Milwaukee , WI 53201-1881 , USA","Department of Electrical and Computer Engineering, Marquette University, PO Box 1881, Milwaukee, WI 53201-1881, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering , Marquette University , PO Box 1881 , Milwaukee , WI 53201-1881 , USA","institution_ids":["https://openalex.org/I102461120"]},{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Marquette University, PO Box 1881, Milwaukee, WI 53201-1881, USA","institution_ids":["https://openalex.org/I102461120"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103354957","display_name":"D. Subbaram Naidu","orcid":null},"institutions":[{"id":"https://openalex.org/I106969075","display_name":"Idaho State University","ror":"https://ror.org/0162z8b04","country_code":"US","type":"education","lineage":["https://openalex.org/I106969075"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"D. Subbaram Naidu","raw_affiliation_strings":["College of Engineering, Campus Box 8060 , Idaho State University , Pocatello , ID 83209 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Engineering, Campus Box 8060 , Idaho State University , Pocatello , ID 83209 , USA","institution_ids":["https://openalex.org/I106969075"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.11657326,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"34","issue":"6","first_page":"403","last_page":"412"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9926999807357788,"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":0.9926999807357788,"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/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.9904000163078308,"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/T11236","display_name":"Control Systems and Identification","score":0.9894000291824341,"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/discrete-time-and-continuous-time","display_name":"Discrete time and continuous time","score":0.8070346117019653},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.5612350106239319},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.540051281452179},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.49612101912498474},{"id":"https://openalex.org/keywords/sampling","display_name":"Sampling (signal processing)","score":0.4916258454322815},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.47678497433662415},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.4578385353088379},{"id":"https://openalex.org/keywords/separation","display_name":"Separation (statistics)","score":0.435931533575058},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.39323097467422485},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.38571852445602417},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.11188027262687683},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1096697449684143},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09328493475914001}],"concepts":[{"id":"https://openalex.org/C55689738","wikidata":"https://www.wikidata.org/wiki/Q15963867","display_name":"Discrete time and continuous time","level":2,"score":0.8070346117019653},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.5612350106239319},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.540051281452179},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.49612101912498474},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.4916258454322815},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.47678497433662415},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4578385353088379},{"id":"https://openalex.org/C2776061190","wikidata":"https://www.wikidata.org/wiki/Q7451805","display_name":"Separation (statistics)","level":2,"score":0.435931533575058},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.39323097467422485},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.38571852445602417},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.11188027262687683},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1096697449684143},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09328493475914001},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207720310001612909","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207720310001612909","pdf_url":null,"source":{"id":"https://openalex.org/S129640837","display_name":"International Journal of Systems Science","issn_l":"0020-7721","issn":["0020-7721","1464-5319"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Systems Science","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W47437515","https://openalex.org/W1515224583","https://openalex.org/W1524707262","https://openalex.org/W1532777065","https://openalex.org/W1582825494","https://openalex.org/W1814021024","https://openalex.org/W1972294015","https://openalex.org/W2031772420","https://openalex.org/W2044837789","https://openalex.org/W2076220135","https://openalex.org/W2145258555","https://openalex.org/W2156768156","https://openalex.org/W4213303927","https://openalex.org/W4252247111","https://openalex.org/W4298290699"],"related_works":["https://openalex.org/W2071676784","https://openalex.org/W4292513318","https://openalex.org/W2287611352","https://openalex.org/W320684304","https://openalex.org/W1509352139","https://openalex.org/W4385464961","https://openalex.org/W4308092240","https://openalex.org/W2060903012","https://openalex.org/W2021161555","https://openalex.org/W4385829936"],"abstract_inverted_index":{"In":[0],"this":[1,20,99],"paper,":[2],"we":[3,76,88],"first":[4],"propose":[5],"a":[6,25,45,51,103,106,122],"modified":[7],"definition":[8],"for":[9,13,115,126],"timescale":[10,22,26,46,104],"separation":[11,23],"ratio":[12],"the":[14,32,41,73,83,90,113,116,130,139,152],"discrete-time":[15,59,74,119,133],"system.":[16],"Then,":[17],"based":[18],"on":[19],"new":[21],"ratio,":[24],"analysis":[27,47],"is":[28,48,63,109,145],"presented":[29,49],"to":[30,55,86,102,111,150],"decompose":[31],"system":[33],"into":[34],"fast":[35],"and":[36,58,79,118,134],"slow":[37],"subsystems.":[38],"Next,":[39],"using":[40,50,67],"difference":[42],"(delta)":[43],"operator,":[44],"unified":[52,100],"formulation":[53],"(applicable":[54],"both":[56],"continuous-time":[57,91,117,135],"systems).":[60],"Furthermore,":[61],"it":[62],"shown":[64],"that":[65],"by":[66,80,95],"simple":[68],"transformations,":[69],"one":[70],"can":[71],"obtain":[72,89],"results":[75],"developed":[77,93],"earlier,":[78],"similarly":[81],"setting":[82],"sampling":[84],"interval":[85],"zero,":[87],"result":[92],"previously":[94],"others.":[96],"Thus,":[97],"with":[98],"approach":[101],"system,":[105],"single":[107],"technique":[108],"sufficient":[110],"develop":[112],"techniques":[114],"systems.":[120],"Having":[121],"pair":[123],"of":[124],"routines":[125],"each":[127],"task":[128],"emphasizes":[129],"differences":[131],"between":[132],"theory":[136],"rather":[137],"than":[138],"similarities.":[140],"An":[141],"F-8":[142],"fighter":[143],"aircraft":[144],"given":[146],"as":[147],"an":[148],"example":[149],"illustrate":[151],"methodology.":[153]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}