{"id":"https://openalex.org/W2921592546","doi":"https://doi.org/10.1109/cdc40024.2019.9029588","title":"Integral Quadratic Constraints: Exact Convergence Rates and Worst-Case Trajectories","display_name":"Integral Quadratic Constraints: Exact Convergence Rates and Worst-Case Trajectories","publication_year":2019,"publication_date":"2019-12-01","ids":{"openalex":"https://openalex.org/W2921592546","doi":"https://doi.org/10.1109/cdc40024.2019.9029588","mag":"2921592546"},"language":"en","primary_location":{"id":"doi:10.1109/cdc40024.2019.9029588","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc40024.2019.9029588","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2019 IEEE 58th Conference on Decision and Control (CDC)","raw_type":"proceedings-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1903.07668","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5035128434","display_name":"Bryan Van Scoy","orcid":"https://orcid.org/0000-0002-8286-2311"},"institutions":[{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]},{"id":"https://openalex.org/I2802999273","display_name":"Wisconsin Institutes for Discovery","ror":"https://ror.org/05gbven85","country_code":"US","type":"nonprofit","lineage":["https://openalex.org/I2802999273"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Bryan Van Scoy","raw_affiliation_strings":["Wisconsin Institute for Discovery, University of Wisconsin\u2013Madison, Madison, WI, USA","University of Wisconsin-Madison, #TAB#"],"affiliations":[{"raw_affiliation_string":"Wisconsin Institute for Discovery, University of Wisconsin\u2013Madison, Madison, WI, USA","institution_ids":["https://openalex.org/I2802999273","https://openalex.org/I135310074"]},{"raw_affiliation_string":"University of Wisconsin-Madison, #TAB#","institution_ids":["https://openalex.org/I135310074"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5016674253","display_name":"Laurent Lessard","orcid":"https://orcid.org/0000-0001-5389-9361"},"institutions":[{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Laurent Lessard","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of Wisconsin\u2013Madison","University of Wisconsin-Madison, #TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Wisconsin\u2013Madison","institution_ids":["https://openalex.org/I135310074"]},{"raw_affiliation_string":"University of Wisconsin-Madison, #TAB#","institution_ids":["https://openalex.org/I135310074"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5035128434"],"corresponding_institution_ids":["https://openalex.org/I135310074","https://openalex.org/I2802999273"],"apc_list":null,"apc_paid":null,"fwci":0.3369,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.56868641,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"3","issue":null,"first_page":"7677","last_page":"7682"},"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":0.9991999864578247,"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":0.9991999864578247,"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":0.9962999820709229,"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/T10805","display_name":"Vehicle Dynamics and Control Systems","score":0.9961000084877014,"subfield":{"id":"https://openalex.org/subfields/2203","display_name":"Automotive 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/quadratic-equation","display_name":"Quadratic equation","score":0.7386223077774048},{"id":"https://openalex.org/keywords/spectral-radius","display_name":"Spectral radius","score":0.7314617037773132},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6160941123962402},{"id":"https://openalex.org/keywords/trajectory","display_name":"Trajectory","score":0.5931127071380615},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.5672168731689453},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5150966048240662},{"id":"https://openalex.org/keywords/radius","display_name":"RADIUS","score":0.46623939275741577},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.43594539165496826},{"id":"https://openalex.org/keywords/lti-system-theory","display_name":"LTI system theory","score":0.4240448772907257},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.411952942609787},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.408047080039978},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.3873838484287262},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2758597135543823},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.19302836060523987},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.1049942672252655},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.0996391773223877},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09683537483215332},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09531450271606445},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.057846009731292725},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.05351996421813965}],"concepts":[{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.7386223077774048},{"id":"https://openalex.org/C140532419","wikidata":"https://www.wikidata.org/wiki/Q249748","display_name":"Spectral radius","level":3,"score":0.7314617037773132},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6160941123962402},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.5931127071380615},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5672168731689453},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5150966048240662},{"id":"https://openalex.org/C178635117","wikidata":"https://www.wikidata.org/wiki/Q747499","display_name":"RADIUS","level":2,"score":0.46623939275741577},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.43594539165496826},{"id":"https://openalex.org/C87698059","wikidata":"https://www.wikidata.org/wiki/Q1808960","display_name":"LTI system theory","level":3,"score":0.4240448772907257},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.411952942609787},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.408047080039978},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.3873838484287262},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2758597135543823},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.19302836060523987},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.1049942672252655},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0996391773223877},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09683537483215332},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09531450271606445},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.057846009731292725},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.05351996421813965},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","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},{"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/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/cdc40024.2019.9029588","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc40024.2019.9029588","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2019 IEEE 58th Conference on Decision and Control (CDC)","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:1903.07668","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1903.07668","pdf_url":"https://arxiv.org/pdf/1903.07668","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":"mag:2921592546","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1903.07668.pdf","pdf_url":null,"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":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1903.07668","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1903.07668","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1903.07668","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1903.07668","pdf_url":"https://arxiv.org/pdf/1903.07668","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"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4088109193","display_name":null,"funder_award_id":"1750162","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6307293017","display_name":null,"funder_award_id":"1710892","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7975498805","display_name":null,"funder_award_id":"1656951","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G848032724","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2921592546.pdf","grobid_xml":"https://content.openalex.org/works/W2921592546.grobid-xml"},"referenced_works_count":20,"referenced_works":["https://openalex.org/W1953100011","https://openalex.org/W1967184028","https://openalex.org/W2003658506","https://openalex.org/W2063493327","https://openalex.org/W2077418568","https://openalex.org/W2095477585","https://openalex.org/W2097460613","https://openalex.org/W2097944741","https://openalex.org/W2115832833","https://openalex.org/W2118550318","https://openalex.org/W2296319761","https://openalex.org/W2333053474","https://openalex.org/W2504806216","https://openalex.org/W2610857016","https://openalex.org/W2914604815","https://openalex.org/W2964102336","https://openalex.org/W4229706427","https://openalex.org/W4250589301","https://openalex.org/W4296926842","https://openalex.org/W6640976022"],"related_works":["https://openalex.org/W3011218186","https://openalex.org/W3080946871","https://openalex.org/W2949746748","https://openalex.org/W2887763427","https://openalex.org/W3205813617","https://openalex.org/W2618714577","https://openalex.org/W2950242339","https://openalex.org/W3112297303","https://openalex.org/W2030533255","https://openalex.org/W2774801765","https://openalex.org/W2067369324","https://openalex.org/W2115910716","https://openalex.org/W2034956685","https://openalex.org/W2951553913","https://openalex.org/W3098020435","https://openalex.org/W3047125623","https://openalex.org/W2042157412","https://openalex.org/W2889795689","https://openalex.org/W3199696287","https://openalex.org/W2127429426"],"abstract_inverted_index":{"We":[0],"consider":[1],"a":[2,16,32],"linear":[3,27],"time-invariant":[4],"system":[5,60],"in":[6],"discrete":[7],"time":[8],"where":[9],"the":[10,25,49,59,69,74,88,97,101],"state":[11],"and":[12,71],"input":[13],"signals":[14],"satisfy":[15,68],"set":[17],"of":[18,35,42,96],"integral":[19],"quadratic":[20],"constraints":[21],"(IQCs).":[22],"Analogous":[23],"to":[24,79,100],"autonomous":[26],"systems":[28],"case,":[29],"we":[30,56,81,91],"define":[31],"new":[33,94],"notion":[34],"spectral":[36,50,75,98],"radius":[37,51,76,99],"that":[38,58,67,86],"exactly":[39],"characterizes":[40],"stability":[41],"this":[43],"system.":[44],"In":[45],"particular,":[46],"(i)":[47],"when":[48,73],"is":[52,61,77],"less":[53],"than":[54],"one,":[55,80],"show":[57],"asymptotically":[62],"stable":[63],"for":[64],"all":[65],"trajectories":[66],"IQCs,":[70],"(ii)":[72],"equal":[78],"construct":[82],"an":[83],"unstable":[84],"trajectory":[85],"satisfies":[87],"IQCs.":[89,105],"Furthermore,":[90],"connect":[92],"our":[93],"definition":[95],"existing":[102],"literature":[103],"on":[104]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}