{"id":"https://openalex.org/W2142687566","doi":"https://doi.org/10.1109/acc.2007.4282315","title":"Further Results on Computing the Distance to Uncontrollability via LMIs","display_name":"Further Results on Computing the Distance to Uncontrollability via LMIs","publication_year":2007,"publication_date":"2007-07-01","ids":{"openalex":"https://openalex.org/W2142687566","doi":"https://doi.org/10.1109/acc.2007.4282315","mag":"2142687566"},"language":"en","primary_location":{"id":"doi:10.1109/acc.2007.4282315","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2007.4282315","pdf_url":null,"source":{"id":"https://openalex.org/S4210168941","display_name":"Proceedings of the ... American Control Conference/Proceedings of the American Control Conference","issn_l":"0743-1619","issn":["0743-1619","2378-5861"],"is_oa":false,"is_in_doaj":false,"is_core":false,"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":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2007 American Control Conference","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/A5042752122","display_name":"Yoshio Ebihara","orcid":"https://orcid.org/0000-0002-9342-1650"},"institutions":[{"id":"https://openalex.org/I22299242","display_name":"Kyoto University","ror":"https://ror.org/02kpeqv85","country_code":"JP","type":"education","lineage":["https://openalex.org/I22299242"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Yoshio Ebihara","raw_affiliation_strings":["Department of Electrical Engineering, Kyoto University, Nishikyo, Kyoto, Japan","Kyoto University, Kyoto"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Kyoto University, Nishikyo, Kyoto, Japan","institution_ids":["https://openalex.org/I22299242"]},{"raw_affiliation_string":"Kyoto University, Kyoto","institution_ids":["https://openalex.org/I22299242"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5001719830","display_name":"Tomomichi Hagiwara","orcid":"https://orcid.org/0000-0002-9212-9551"},"institutions":[{"id":"https://openalex.org/I22299242","display_name":"Kyoto University","ror":"https://ror.org/02kpeqv85","country_code":"JP","type":"education","lineage":["https://openalex.org/I22299242"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Tomomichi Hagiwara","raw_affiliation_strings":["Department of Electrical Engineering, Kyoto University, Nishikyo, Kyoto, Japan","Kyoto University, Kyoto"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Kyoto University, Nishikyo, Kyoto, Japan","institution_ids":["https://openalex.org/I22299242"]},{"raw_affiliation_string":"Kyoto University, Kyoto","institution_ids":["https://openalex.org/I22299242"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5042752122"],"corresponding_institution_ids":["https://openalex.org/I22299242"],"apc_list":null,"apc_paid":null,"fwci":0.6316,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.59574468,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"5","issue":null,"first_page":"6157","last_page":"6162"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9991999864578247,"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"}},"topics":[{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9991999864578247,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9977999925613403,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.9954000115394592,"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/rank","display_name":"Rank (graph theory)","score":0.5472630262374878},{"id":"https://openalex.org/keywords/semidefinite-programming","display_name":"Semidefinite programming","score":0.5337067246437073},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5175566077232361},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4845484793186188},{"id":"https://openalex.org/keywords/duality","display_name":"Duality (order theory)","score":0.4638044834136963},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4624190032482147},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4380246698856354},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4264557361602783},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.42317262291908264},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4198628067970276},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3092418611049652},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.18632733821868896}],"concepts":[{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5472630262374878},{"id":"https://openalex.org/C101901036","wikidata":"https://www.wikidata.org/wiki/Q2269096","display_name":"Semidefinite programming","level":2,"score":0.5337067246437073},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5175566077232361},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4845484793186188},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.4638044834136963},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4624190032482147},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4380246698856354},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4264557361602783},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.42317262291908264},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4198628067970276},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3092418611049652},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.18632733821868896},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","level":1,"score":0.0},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/acc.2007.4282315","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2007.4282315","pdf_url":null,"source":{"id":"https://openalex.org/S4210168941","display_name":"Proceedings of the ... American Control Conference/Proceedings of the American Control Conference","issn_l":"0743-1619","issn":["0743-1619","2378-5861"],"is_oa":false,"is_in_doaj":false,"is_core":false,"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":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2007 American Control Conference","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W1510134586","https://openalex.org/W1588998206","https://openalex.org/W1628175921","https://openalex.org/W1967073510","https://openalex.org/W2036031971","https://openalex.org/W2046473141","https://openalex.org/W2057000602","https://openalex.org/W2077418568","https://openalex.org/W2082411704","https://openalex.org/W2102914244","https://openalex.org/W2103313140","https://openalex.org/W2108489060","https://openalex.org/W2115832833","https://openalex.org/W2123353000","https://openalex.org/W2124032294","https://openalex.org/W2134046186","https://openalex.org/W2151177951","https://openalex.org/W2157771090","https://openalex.org/W2164349943","https://openalex.org/W4231245785","https://openalex.org/W4242975128","https://openalex.org/W6635035695"],"related_works":["https://openalex.org/W1983756092","https://openalex.org/W2381295697","https://openalex.org/W2385886188","https://openalex.org/W2378309693","https://openalex.org/W579949368","https://openalex.org/W1788812054","https://openalex.org/W4225784730","https://openalex.org/W3122644328","https://openalex.org/W2164080590","https://openalex.org/W1019837216"],"abstract_inverted_index":{"This":[0,30,123],"paper":[1],"concerns":[2],"the":[3,6,40,63,67,70,83,109,114,120,149,156,160,164,169,173,180,184,198,201,224,227,230,234,242,255,260],"computation":[4,44,240],"of":[5,11,39,66,73,163,183,186,223,233,241,254],"distance":[7],"to":[8,61,103,171,213,248],"uncontrollability":[9],"(DTUC)":[10],"a":[12,36,91,105],"given":[13],"controllable":[14],"pair":[15,261],"A":[16],"isin":[17,24],"C":[18,25],"<sup":[19,26,188,192],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[20,27,189,193],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">ntimesn</sup>":[21],"and":[22,46,131,217,229,251],"B":[23],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">ntimesm</sup>":[28],".":[29],"problem":[31,170,209,216,258],"can":[32,86,140,210],"be":[33,87,211],"regarded":[34],"as":[35],"special":[37],"case":[38],"structured":[41],"singular":[42],"value":[43],"problems":[45,147],"motivated":[47],"from":[48],"this":[49,74,98,208,239],"fact,":[50],"in":[51,129,159],"our":[52],"preceding":[53],"work,":[54],"we":[55,76,132,139,167,205],"derived":[56],"an":[57,249],"semidefinite":[58],"program":[59],"(SDP)":[60],"compute":[62,172],"lower":[64,84,116,181,202],"bounds":[65,85,203],"DTUC.":[68,122],"In":[69,96,221],"first":[71],"part":[72,162],"paper,":[75,166],"show":[77,134],"via":[78],"convex":[79],"duality":[80],"theory":[81],"that":[82,138,178,207],"computed":[88,115],"by":[89],"solving":[90],"very":[92],"concise":[93],"dual":[94,99,110],"SDP.":[95],"particular,":[97],"SDP":[100,199],"enables":[101],"us":[102],"derive":[104],"rank":[106,124],"condition":[107,125],"on":[108,197],"variable":[111],"under":[112],"which":[113],"bound":[117,182],"coincides":[118],"with":[119],"exact":[121],"is":[126],"surely":[127],"effective":[128,250],"practice,":[130],"will":[133],"thorough":[135],"numerical":[136,231],"examples":[137],"obtain":[141],"exactness":[142,152],"certificate":[143],"even":[144],"for":[145,200,259],"those":[146],"where":[148],"common":[150],"rank-one":[151],"principle":[153],"fails.":[154],"On":[155],"other":[157],"hand,":[158],"second":[161],"present":[165],"consider":[168],"similarity":[174,243],"transformation":[175,244],"matrix":[176,245],"T":[177],"maximizes":[179],"DTUC":[185,228],"(T":[187],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">-1</sup>":[190,194],"AT,T":[191],"B).":[195,263],"Based":[196],"computation,":[204],"clarify":[206],"reduced":[212],"generalized":[214],"eigenvalue":[215],"thus":[218],"solved":[219],"efficiently.":[220],"view":[222],"correlation":[225],"between":[226],"difficulties":[232],"associated":[235],"pole":[236,256],"placement":[237,257],"problem,":[238],"would":[246],"lead":[247],"efficient":[252],"conditioning":[253],"(A,":[262]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
