{"id":"https://openalex.org/W2609364098","doi":"https://doi.org/10.1080/00207179.2018.1465205","title":"Conditions for the equivalence between IQC and graph separation stability results","display_name":"Conditions for the equivalence between IQC and graph separation stability results","publication_year":2018,"publication_date":"2018-04-18","ids":{"openalex":"https://openalex.org/W2609364098","doi":"https://doi.org/10.1080/00207179.2018.1465205","mag":"2609364098"},"language":"en","primary_location":{"id":"doi:10.1080/00207179.2018.1465205","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207179.2018.1465205","pdf_url":null,"source":{"id":"https://openalex.org/S88061139","display_name":"International Journal of Control","issn_l":"0020-7179","issn":["0020-7179","1366-5820"],"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 Control","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://research.manchester.ac.uk/en/publications/c9ddfbd3-2e22-4063-b86a-584b7d026fda","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5024320684","display_name":"Joaqu\u00edn Carrasco","orcid":"https://orcid.org/0000-0002-7499-6408"},"institutions":[{"id":"https://openalex.org/I28407311","display_name":"University of Manchester","ror":"https://ror.org/027m9bs27","country_code":"GB","type":"education","lineage":["https://openalex.org/I28407311"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Joaquin Carrasco","raw_affiliation_strings":["Control Systems Centre, School of Electrical and Electronic Engineering, The University of Manchester , Manchester, UK","Control Systems Centre, School of Electrical and Electronic Engineering, The University of Manchester\n, Manchester, UK"],"affiliations":[{"raw_affiliation_string":"Control Systems Centre, School of Electrical and Electronic Engineering, The University of Manchester , Manchester, UK","institution_ids":["https://openalex.org/I28407311"]},{"raw_affiliation_string":"Control Systems Centre, School of Electrical and Electronic Engineering, The University of Manchester\n, Manchester, UK","institution_ids":["https://openalex.org/I28407311"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5009028512","display_name":"Peter Seiler","orcid":"https://orcid.org/0000-0003-3423-1109"},"institutions":[{"id":"https://openalex.org/I130238516","display_name":"University of Minnesota","ror":"https://ror.org/017zqws13","country_code":"US","type":"education","lineage":["https://openalex.org/I130238516"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Peter Seiler","raw_affiliation_strings":["Aerospace Engineering and Mechanics Department, University of Minnesota , Minneapolis, MN, USA","Aerospace Engineering and Mechanics Department, University of Minnesota\n, Minneapolis, MN, USA"],"affiliations":[{"raw_affiliation_string":"Aerospace Engineering and Mechanics Department, University of Minnesota , Minneapolis, MN, USA","institution_ids":["https://openalex.org/I130238516"]},{"raw_affiliation_string":"Aerospace Engineering and Mechanics Department, University of Minnesota\n, Minneapolis, MN, USA","institution_ids":["https://openalex.org/I130238516"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5024320684"],"corresponding_institution_ids":["https://openalex.org/I28407311"],"apc_list":null,"apc_paid":null,"fwci":1.4964,"has_fulltext":false,"cited_by_count":19,"citation_normalized_percentile":{"value":0.82594329,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"92","issue":"12","first_page":"2899","last_page":"2906"},"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":0.9945999979972839,"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":0.9945999979972839,"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":0.9940999746322632,"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/T10690","display_name":"Vibration Control and Rheological Fluids","score":0.9882000088691711,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural 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/mathematics","display_name":"Mathematics","score":0.7253859639167786},{"id":"https://openalex.org/keywords/frequency-domain","display_name":"Frequency domain","score":0.6607826948165894},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5321986079216003},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.5279480814933777},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.5171467661857605},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4342584013938904},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.4259689748287201},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4100501537322998},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.39520370960235596},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.378018856048584},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2815662622451782},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.2774146795272827},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2669762969017029},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2125469446182251}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7253859639167786},{"id":"https://openalex.org/C19118579","wikidata":"https://www.wikidata.org/wiki/Q786423","display_name":"Frequency domain","level":2,"score":0.6607826948165894},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5321986079216003},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.5279480814933777},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.5171467661857605},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4342584013938904},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.4259689748287201},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4100501537322998},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.39520370960235596},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.378018856048584},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2815662622451782},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2774146795272827},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2669762969017029},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2125469446182251},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","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/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","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},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1080/00207179.2018.1465205","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207179.2018.1465205","pdf_url":null,"source":{"id":"https://openalex.org/S88061139","display_name":"International Journal of Control","issn_l":"0020-7179","issn":["0020-7179","1366-5820"],"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 Control","raw_type":"journal-article"},{"id":"pmh:oai:pure.atira.dk:openaire/c9ddfbd3-2e22-4063-b86a-584b7d026fda","is_oa":true,"landing_page_url":"https://research.manchester.ac.uk/en/publications/c9ddfbd3-2e22-4063-b86a-584b7d026fda","pdf_url":null,"source":{"id":"https://openalex.org/S4306400662","display_name":"Research Explorer (The University of Manchester)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I28407311","host_organization_name":"University of Manchester","host_organization_lineage":["https://openalex.org/I28407311"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Carrasco, J & Seiler, P 2018, 'Conditions for the equivalence between IQC and graph separation stability results', International Journal of Control. https://doi.org/10.1080/00207179.2018.1465205","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:arXiv.org:1704.04816","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1704.04816","pdf_url":"https://arxiv.org/pdf/1704.04816","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:pure.atira.dk:publications/c9ddfbd3-2e22-4063-b86a-584b7d026fda","is_oa":false,"landing_page_url":"https://www.research.manchester.ac.uk/portal/en/publications/conditions-for-the-equivalence-between-iqc-and-graph-separation-stability-results(c9ddfbd3-2e22-4063-b86a-584b7d026fda).html","pdf_url":null,"source":{"id":"https://openalex.org/S4306400662","display_name":"Research Explorer (The University of Manchester)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I28407311","host_organization_name":"University of Manchester","host_organization_lineage":["https://openalex.org/I28407311"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""}],"best_oa_location":{"id":"pmh:oai:pure.atira.dk:openaire/c9ddfbd3-2e22-4063-b86a-584b7d026fda","is_oa":true,"landing_page_url":"https://research.manchester.ac.uk/en/publications/c9ddfbd3-2e22-4063-b86a-584b7d026fda","pdf_url":null,"source":{"id":"https://openalex.org/S4306400662","display_name":"Research Explorer (The University of Manchester)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I28407311","host_organization_name":"University of Manchester","host_organization_lineage":["https://openalex.org/I28407311"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Carrasco, J & Seiler, P 2018, 'Conditions for the equivalence between IQC and graph separation stability results', International Journal of Control. https://doi.org/10.1080/00207179.2018.1465205","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W66870049","https://openalex.org/W601102923","https://openalex.org/W1479905714","https://openalex.org/W1482934371","https://openalex.org/W1538036351","https://openalex.org/W1691404827","https://openalex.org/W1887006513","https://openalex.org/W1968726193","https://openalex.org/W2003658506","https://openalex.org/W2026769037","https://openalex.org/W2063493327","https://openalex.org/W2097944741","https://openalex.org/W2104439410","https://openalex.org/W2112446957","https://openalex.org/W2116511711","https://openalex.org/W2125301473","https://openalex.org/W2127768514","https://openalex.org/W2140109343","https://openalex.org/W2160188132","https://openalex.org/W2163101083","https://openalex.org/W2164904527","https://openalex.org/W2288702566","https://openalex.org/W2401135644","https://openalex.org/W2565271410","https://openalex.org/W3034208633","https://openalex.org/W3160954918","https://openalex.org/W4253020970","https://openalex.org/W4299810010","https://openalex.org/W4395684075"],"related_works":["https://openalex.org/W2794559785","https://openalex.org/W1754499339","https://openalex.org/W2013873776","https://openalex.org/W2950281908","https://openalex.org/W2963117165","https://openalex.org/W2084977674","https://openalex.org/W2583828359","https://openalex.org/W3102011585","https://openalex.org/W2037667647","https://openalex.org/W2954309532"],"abstract_inverted_index":{"This":[0],"paper":[1],"provides":[2],"a":[3,24,49,96,116,132],"link":[4],"between":[5,20,119],"time-domain":[6,68,109],"and":[7,125],"frequency-domain":[8,35,64,89,105],"stability":[9,21],"results":[10,22,58,121],"in":[11,32],"the":[12,18,38,53,60,63,74,81,87,113,120,139],"literature.":[13],"Specifically,":[14],"we":[15,134],"focus":[16],"on":[17,77],"comparison":[19,118],"for":[23,52],"feedback":[25],"interconnection":[26],"of":[27,34,62,73,80,86],"two":[28,88],"nonlinear":[29],"systems":[30],"stated":[31],"terms":[33],"conditions.":[36,69,90,110],"While":[37],"integral":[39],"quadratic":[40],"constrain":[41],"(IQC)":[42],"theorem":[43,141],"can":[44],"cope":[45],"with":[46],"them":[47],"via":[48],"homotopy":[50],"argument":[51],"Lurye":[54],"problem,":[55],"graph":[56],"separation":[57,126],"require":[59],"transformation":[61],"conditions":[65,106,138],"into":[66,107],"truncated":[67,108],"To":[70],"date,":[71],"much":[72],"literature":[75],"focuses":[76],"\u2018hard\u2019":[78],"factorisations":[79],"multiplier,":[82],"considering":[83],"only":[84],"one":[85],"Here":[91],"it":[92],"is":[93,100,128],"shown":[94],"that":[95],"symmetric,":[97],"\u2018doubly-hard\u2019":[98],"factorisation":[99],"required":[101],"to":[102],"convert":[103],"both":[104],"By":[111],"using":[112],"appropriate":[114],"factorisation,":[115],"novel":[117],"obtained":[122],"by":[123],"IQC":[124,140],"theories":[127],"then":[129],"provided.":[130],"As":[131],"result,":[133],"identify":[135],"under":[136],"what":[137],"may":[142],"provide":[143],"some":[144],"advantage.":[145]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2020-11-23T00:00:00"}