{"id":"https://openalex.org/W2132677492","doi":"https://doi.org/10.1109/tac.2009.2017087","title":"Convex Matrix Inequalities Versus Linear Matrix Inequalities","display_name":"Convex Matrix Inequalities Versus Linear Matrix Inequalities","publication_year":2009,"publication_date":"2009-05-01","ids":{"openalex":"https://openalex.org/W2132677492","doi":"https://doi.org/10.1109/tac.2009.2017087","mag":"2132677492"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2009.2017087","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2009.2017087","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","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/A5080005590","display_name":"J. William Helton","orcid":null},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"J.W. Helton","raw_affiliation_strings":["Department of Mathematics, University of California, San Diego, La Jolla, CA, USA","[Dept. of Math., Univ. of California, San Diego, La Jolla, CA]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of California, San Diego, La Jolla, CA, USA","institution_ids":["https://openalex.org/I36258959"]},{"raw_affiliation_string":"[Dept. of Math., Univ. of California, San Diego, La Jolla, CA]","institution_ids":["https://openalex.org/I36258959"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5034080046","display_name":"Scott McCullough","orcid":"https://orcid.org/0000-0001-6530-7845"},"institutions":[{"id":"https://openalex.org/I33213144","display_name":"University of Florida","ror":"https://ror.org/02y3ad647","country_code":"US","type":"education","lineage":["https://openalex.org/I33213144"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"S. McCullough","raw_affiliation_strings":["Department of Mathematics, University of Florida, Gainesville, FL, USA","Dept. of Math., Univ. of Florida, Gainesville, FL"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Florida, Gainesville, FL, USA","institution_ids":["https://openalex.org/I33213144"]},{"raw_affiliation_string":"Dept. of Math., Univ. of Florida, Gainesville, FL","institution_ids":["https://openalex.org/I33213144"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026457502","display_name":"Mihai Putinar","orcid":"https://orcid.org/0000-0003-1604-1651"},"institutions":[{"id":"https://openalex.org/I154570441","display_name":"University of California, Santa Barbara","ror":"https://ror.org/02t274463","country_code":"US","type":"education","lineage":["https://openalex.org/I154570441"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"M. Putinar","raw_affiliation_strings":["Department of Mathematics, University of California,\uc2a0Santa Barbara, Santa Barbara, CA, USA","Dept. of Math., Univ. of California, Santa Barbara, Santa Barbara, CA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of California,\uc2a0Santa Barbara, Santa Barbara, CA, USA","institution_ids":["https://openalex.org/I154570441"]},{"raw_affiliation_string":"Dept. of Math., Univ. of California, Santa Barbara, Santa Barbara, CA","institution_ids":["https://openalex.org/I154570441"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5030513428","display_name":"Victor Vinnikov","orcid":"https://orcid.org/0000-0003-2965-1408"},"institutions":[{"id":"https://openalex.org/I124227911","display_name":"Ben-Gurion University of the Negev","ror":"https://ror.org/05tkyf982","country_code":"IL","type":"education","lineage":["https://openalex.org/I124227911"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"V. Vinnikov","raw_affiliation_strings":["Department of Mathematics, Ben-Gurion University of the Negev, Beersheba, Israel","[Dept. of Math., Ben Gurion Univ. of the Negev, Beer-Sheva]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Ben-Gurion University of the Negev, Beersheba, Israel","institution_ids":["https://openalex.org/I124227911"]},{"raw_affiliation_string":"[Dept. of Math., Ben Gurion Univ. of the Negev, Beer-Sheva]","institution_ids":["https://openalex.org/I124227911"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.819,"has_fulltext":false,"cited_by_count":61,"citation_normalized_percentile":{"value":0.93592786,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"54","issue":"5","first_page":"952","last_page":"964"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9997000098228455,"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":0.9997000098228455,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"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":0.9977999925613403,"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/mathematics","display_name":"Mathematics","score":0.7720969915390015},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.7345345616340637},{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.7216326594352722},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5474156141281128},{"id":"https://openalex.org/keywords/convex-analysis","display_name":"Convex analysis","score":0.466691792011261},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.4496300518512726},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.4341175854206085},{"id":"https://openalex.org/keywords/linear-matrix-inequality","display_name":"Linear matrix inequality","score":0.43113037943840027},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.41599640250205994},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.3836744725704193},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.32549333572387695},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2312883734703064},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.22437214851379395},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06918501853942871}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7720969915390015},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.7345345616340637},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.7216326594352722},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5474156141281128},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.466691792011261},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4496300518512726},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.4341175854206085},{"id":"https://openalex.org/C201829737","wikidata":"https://www.wikidata.org/wiki/Q2022760","display_name":"Linear matrix inequality","level":2,"score":0.43113037943840027},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.41599640250205994},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.3836744725704193},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.32549333572387695},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2312883734703064},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.22437214851379395},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06918501853942871},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tac.2009.2017087","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2009.2017087","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.4399999976158142}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":48,"referenced_works":["https://openalex.org/W574556491","https://openalex.org/W1000262507","https://openalex.org/W1482736558","https://openalex.org/W1506437980","https://openalex.org/W1507415131","https://openalex.org/W1527351491","https://openalex.org/W1539838732","https://openalex.org/W1588868664","https://openalex.org/W1632601927","https://openalex.org/W1868559974","https://openalex.org/W1966069595","https://openalex.org/W1967344706","https://openalex.org/W1974962384","https://openalex.org/W2001033871","https://openalex.org/W2001618379","https://openalex.org/W2003733377","https://openalex.org/W2005916892","https://openalex.org/W2008973530","https://openalex.org/W2011012260","https://openalex.org/W2024340911","https://openalex.org/W2025202934","https://openalex.org/W2055559161","https://openalex.org/W2055561145","https://openalex.org/W2063191289","https://openalex.org/W2083557522","https://openalex.org/W2088104180","https://openalex.org/W2104671712","https://openalex.org/W2122264270","https://openalex.org/W2124343650","https://openalex.org/W2126197766","https://openalex.org/W2128834174","https://openalex.org/W2150044500","https://openalex.org/W2155263740","https://openalex.org/W2417903161","https://openalex.org/W2463908258","https://openalex.org/W2597202805","https://openalex.org/W2888734319","https://openalex.org/W2952434730","https://openalex.org/W2962725330","https://openalex.org/W3106367349","https://openalex.org/W3195133498","https://openalex.org/W4242337769","https://openalex.org/W4250950881","https://openalex.org/W4299599836","https://openalex.org/W6635139765","https://openalex.org/W6644220552","https://openalex.org/W6656298687","https://openalex.org/W6675603297"],"related_works":["https://openalex.org/W4300919033","https://openalex.org/W2105325102","https://openalex.org/W2143181606","https://openalex.org/W2092244978","https://openalex.org/W4378552409","https://openalex.org/W1968149708","https://openalex.org/W4385444493","https://openalex.org/W1967606281","https://openalex.org/W2031642643","https://openalex.org/W4297899479"],"abstract_inverted_index":{"Most":[0,123],"linear":[1,25,88],"control":[2,129],"problems":[3,21,33],"lead":[4],"directly":[5],"to":[6],"matrix":[7,26,121],"inequalities":[8,27],"(MIs).":[9],"Many":[10],"of":[11,20,37,40,87,109,124,128,142,179],"these":[12],"are":[13,22,76,82,106,131,140],"badly":[14],"behaved":[15],"but":[16],"a":[17,41,46,62,101,117],"classical":[18],"core":[19],"expressible":[23],"as":[24],"(LMIs).":[28],"In":[29],"many":[30],"engineering":[31],"systems":[32,89],"convexity":[34,63],"has":[35],"all":[36],"the":[38,59,104,114,125,161,177],"advantages":[39],"LMI.":[42],"Since":[43],"LMIs":[44,77],"have":[45,137],"structure":[47],"which":[48,119,139],"is":[49,58,100,155],"seemingly":[50],"much":[51,73],"more":[52,74],"rigid":[53],"than":[54,70,78],"convex":[55,79,164],"MIs,":[56],"there":[57],"hope":[60],"that":[61],"based":[64],"theory":[65,130],"will":[66],"be":[67],"less":[68],"restrictive":[69,75],"LMIs.":[71,167],"How":[72],"MIs?":[80],"There":[81],"two":[83,145],"fundamentally":[84],"different":[85],"classes":[86,146],"problems:":[90],"dimension":[91,94,97,132],"free":[92,98],"and":[93,111,150,166,172],"dependent.":[95],"A":[96],"MI":[99,102],"where":[103],"unknowns":[105,138],"g":[107],"-tuples":[108],"matrices":[110],"appear":[112],"in":[113,116,157,176],"formulas":[115],"manner":[118],"respects":[120],"multiplication.":[122],"classic":[126],"Mis":[127,136,165],"free.":[133],"Dimension":[134],"dependent":[135],"tuples":[141],"numbers.":[143],"The":[144,168],"behave":[147],"very":[148],"differently":[149],"this":[151],"survey":[152],"describes":[153],"what":[154],"known":[156],"each":[158],"case":[159],"about":[160],"relation":[162],"between":[163],"proof":[169],"techniques":[170],"involve":[171],"necessitate":[173],"new":[174],"developments":[175],"field":[178],"semialgebraic":[180],"geometry.":[181]},"counts_by_year":[{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":23},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":8},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":6}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}