{"id":"https://openalex.org/W1590778455","doi":"https://doi.org/10.23919/ecc.1999.7100089","title":"Lyapunov stability theory for linear repetitive processes \u2014 The 2D equation approach","display_name":"Lyapunov stability theory for linear repetitive processes \u2014 The 2D equation approach","publication_year":1999,"publication_date":"1999-08-01","ids":{"openalex":"https://openalex.org/W1590778455","doi":"https://doi.org/10.23919/ecc.1999.7100089","mag":"1590778455"},"language":"en","primary_location":{"id":"doi:10.23919/ecc.1999.7100089","is_oa":false,"landing_page_url":"https://doi.org/10.23919/ecc.1999.7100089","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"1999 European Control Conference (ECC)","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/A5000533166","display_name":"S E Benton","orcid":null},"institutions":[{"id":"https://openalex.org/I43439940","display_name":"University of Southampton","ror":"https://ror.org/01ryk1543","country_code":"GB","type":"education","lineage":["https://openalex.org/I43439940"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"S. E. Benton","raw_affiliation_strings":["University of Southampton, Southampton, Hampshire, GB","Department of Electronics and Computer Science, University of Southampton, Southampton SO17 1BJ, U.K"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Southampton, Southampton, Hampshire, GB","institution_ids":["https://openalex.org/I43439940"]},{"raw_affiliation_string":"Department of Electronics and Computer Science, University of Southampton, Southampton SO17 1BJ, U.K","institution_ids":["https://openalex.org/I43439940"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5081788754","display_name":"Eric Rogers","orcid":"https://orcid.org/0000-0003-0179-9398"},"institutions":[{"id":"https://openalex.org/I43439940","display_name":"University of Southampton","ror":"https://ror.org/01ryk1543","country_code":"GB","type":"education","lineage":["https://openalex.org/I43439940"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"E. Rogers","raw_affiliation_strings":["University of Southampton, Southampton, Hampshire, GB","Department of Electronics and Computer Science, University of Southampton, Southampton SO17 1BJ, U.K"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Southampton, Southampton, Hampshire, GB","institution_ids":["https://openalex.org/I43439940"]},{"raw_affiliation_string":"Department of Electronics and Computer Science, University of Southampton, Southampton SO17 1BJ, U.K","institution_ids":["https://openalex.org/I43439940"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5109221856","display_name":"D.H. Owens","orcid":"https://orcid.org/0009-0008-3770-8551"},"institutions":[{"id":"https://openalex.org/I91136226","display_name":"University of Sheffield","ror":"https://ror.org/05krs5044","country_code":"GB","type":"education","lineage":["https://openalex.org/I91136226"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"D. H. Owens","raw_affiliation_strings":["The University of Sheffield, Sheffield, Sheffield, GB","Department of Automatic Control and Systems Engineering University of Sheffield, Mappin Street, Sheffield, S1 3JD, U.K"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The University of Sheffield, Sheffield, Sheffield, GB","institution_ids":["https://openalex.org/I91136226"]},{"raw_affiliation_string":"Department of Automatic Control and Systems Engineering University of Sheffield, Mappin Street, Sheffield, S1 3JD, U.K","institution_ids":["https://openalex.org/I91136226"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.7929,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.7151228,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"4768","last_page":"4773"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10791","display_name":"Advanced Control Systems Optimization","score":0.9975000023841858,"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/T10791","display_name":"Advanced Control Systems Optimization","score":0.9975000023841858,"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/T11749","display_name":"Iterative Learning Control Systems","score":0.9973000288009644,"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/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.994700014591217,"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/lyapunov-equation","display_name":"Lyapunov equation","score":0.6014230251312256},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5517428517341614},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.5140799283981323},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.5077663064002991},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.4574550688266754},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4288055896759033},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3974856436252594},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.37796705961227417},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.24599379301071167},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.23013702034950256},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12398940324783325},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09084427356719971},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.07290303707122803}],"concepts":[{"id":"https://openalex.org/C25854792","wikidata":"https://www.wikidata.org/wiki/Q1028945","display_name":"Lyapunov equation","level":4,"score":0.6014230251312256},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5517428517341614},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.5140799283981323},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.5077663064002991},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.4574550688266754},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4288055896759033},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3974856436252594},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.37796705961227417},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.24599379301071167},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.23013702034950256},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12398940324783325},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09084427356719971},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.07290303707122803},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.23919/ecc.1999.7100089","is_oa":false,"landing_page_url":"https://doi.org/10.23919/ecc.1999.7100089","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"1999 European Control Conference (ECC)","raw_type":"proceedings-article"},{"id":"pmh:oai:eprints.soton.ac.uk:252474","is_oa":false,"landing_page_url":"https://eprints.soton.ac.uk/252474/","pdf_url":null,"source":{"id":"https://openalex.org/S4306401019","display_name":"ePrints Soton (University of Southampton)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I43439940","host_organization_name":"University of Southampton","host_organization_lineage":["https://openalex.org/I43439940"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Conference or Workshop Item"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W1544575528","https://openalex.org/W1979981132","https://openalex.org/W1989099401","https://openalex.org/W2019262091","https://openalex.org/W2031390963","https://openalex.org/W2036366356","https://openalex.org/W2079115067","https://openalex.org/W2125014108","https://openalex.org/W2157192413","https://openalex.org/W2166180798"],"related_works":["https://openalex.org/W2349796700","https://openalex.org/W2383986032","https://openalex.org/W2030955003","https://openalex.org/W2374426356","https://openalex.org/W2059628530","https://openalex.org/W2164487476","https://openalex.org/W3194517843","https://openalex.org/W1977987201","https://openalex.org/W2106169668","https://openalex.org/W2534107666"],"abstract_inverted_index":{"This":[0],"paper":[1],"develops":[2],"the":[3,14,33,55,70,95,111],"basis":[4],"of":[5,17,25,44,79],"a":[6,51,77],"so-called":[7,34],"2D":[8,71,96],"Lyapunov":[9,36,56,72,97],"equation":[10,27,37,57,73,98],"based":[11],"approach":[12],"to":[13,32,54,102,108,129],"stability":[15,80,104],"analysis":[16],"discrete":[18,62],"linear":[19,63],"repetitive":[20],"processes.":[21],"The":[22],"key":[23],"feature":[24],"this":[26,88],"is":[28,40,67,82,91],"that,":[29],"in":[30,42,75,110],"contrast":[31],"ID":[35],"approach,":[38],"it":[39,66,90],"defined":[41],"terms":[43],"matrices":[45],"with":[46],"constant":[47],"entries":[48],"and":[49,106],"has":[50],"\u2018similar\u2019":[52],"structure":[53],"for":[58,118,127],"standard,":[59],"or":[60],"ID,":[61],"systems.":[64],"Here":[65],"shown":[68,93],"that":[69],"gives,":[74],"general,":[76],"characterization":[78],"which":[81,119],"sufficient":[83],"but":[84],"not":[85],"necessary.":[86],"Despite":[87],"deficiency,":[89],"also":[92,135],"how":[94],"can":[99],"be":[100],"used":[101],"characterize":[103],"margins":[105],"robustness":[107],"uncertainty":[109],"model":[112],"description":[113],"\u2014":[114],"very":[115],"important":[116],"topics":[117],"few":[120],"results":[121],"are":[122,134],"currently":[123],"available.":[124],"Some":[125],"areas":[126],"short":[128],"medium":[130],"term":[131],"further":[132],"research":[133],"briefly":[136],"noted.":[137]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}