{"id":"https://openalex.org/W2106093427","doi":"https://doi.org/10.1137/050628982","title":"Distance to Uncontrollability for Convex Processes","display_name":"Distance to Uncontrollability for Convex Processes","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W2106093427","doi":"https://doi.org/10.1137/050628982","mag":"2106093427"},"language":"en","primary_location":{"id":"doi:10.1137/050628982","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050628982","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","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/A5081400874","display_name":"Adrian S. Lewis","orcid":"https://orcid.org/0000-0002-1785-1106"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Adrian Lewis","raw_affiliation_strings":["School of Operations Research and Information Engineering"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Operations Research and Information Engineering","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111442239","display_name":"Ren\u00e9 Henrion","orcid":null},"institutions":[{"id":"https://openalex.org/I4210092021","display_name":"Weierstrass Institute for Applied Analysis and Stochastics","ror":"https://ror.org/00h1x4t21","country_code":"DE","type":"facility","lineage":["https://openalex.org/I315704651","https://openalex.org/I4210092021"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Ren\u00e9 Henrion","raw_affiliation_strings":["Weierstrass Institute for Applied Analysis and Stochastics"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Weierstrass Institute for Applied Analysis and Stochastics","institution_ids":["https://openalex.org/I4210092021"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5082203816","display_name":"Alberto Seeger","orcid":"https://orcid.org/0000-0003-3114-7817"},"institutions":[{"id":"https://openalex.org/I4210155549","display_name":"Laboratoire de Math\u00e9matiques Blaise Pascal","ror":"https://ror.org/05sd5r855","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I198244214","https://openalex.org/I4210141950","https://openalex.org/I4210155549"]},{"id":"https://openalex.org/I4405266840","display_name":"Laboratoire de Math\u00e9matiques d'Avignon","ror":"https://ror.org/000d7xf38","country_code":"FR","type":"education","lineage":["https://openalex.org/I198415970","https://openalex.org/I4405266840"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Alberto Seeger","raw_affiliation_strings":["EA2151 Laboratoire de Math\u00e9matiques d'Avignon"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"EA2151 Laboratoire de Math\u00e9matiques d'Avignon","institution_ids":["https://openalex.org/I4210155549","https://openalex.org/I4405266840"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.2502,"has_fulltext":false,"cited_by_count":17,"citation_normalized_percentile":{"value":0.93048674,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"45","issue":"1","first_page":"26","last_page":"50"},"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":0.9984999895095825,"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":0.9984999895095825,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9912999868392944,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9896000027656555,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/controllability","display_name":"Controllability","score":0.8643144965171814},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8236135840415955},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.6088711619377136},{"id":"https://openalex.org/keywords/linear-matrix-inequality","display_name":"Linear matrix inequality","score":0.5503940582275391},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.49705198407173157},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.49625903367996216},{"id":"https://openalex.org/keywords/rendering","display_name":"Rendering (computer graphics)","score":0.45485830307006836},{"id":"https://openalex.org/keywords/differential-inclusion","display_name":"Differential inclusion","score":0.44476330280303955},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.4344889521598816},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.4288782477378845},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3284044861793518},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.27584391832351685},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.21968945860862732},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.18714794516563416},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.13536879420280457},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1124337911605835}],"concepts":[{"id":"https://openalex.org/C48209547","wikidata":"https://www.wikidata.org/wiki/Q1331104","display_name":"Controllability","level":2,"score":0.8643144965171814},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8236135840415955},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.6088711619377136},{"id":"https://openalex.org/C201829737","wikidata":"https://www.wikidata.org/wiki/Q2022760","display_name":"Linear matrix inequality","level":2,"score":0.5503940582275391},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.49705198407173157},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.49625903367996216},{"id":"https://openalex.org/C205711294","wikidata":"https://www.wikidata.org/wiki/Q176953","display_name":"Rendering (computer graphics)","level":2,"score":0.45485830307006836},{"id":"https://openalex.org/C70834904","wikidata":"https://www.wikidata.org/wiki/Q1054638","display_name":"Differential inclusion","level":2,"score":0.44476330280303955},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.4344889521598816},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.4288782477378845},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3284044861793518},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.27584391832351685},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.21968945860862732},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.18714794516563416},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.13536879420280457},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1124337911605835},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/050628982","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050628982","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.484.2208","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.484.2208","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://legacy.orie.cornell.edu/aslewis/publications/06-distance.pdf","raw_type":"text"},{"id":"pmh:oai:HAL:hal-02179211v1","is_oa":false,"landing_page_url":"https://hal.science/hal-02179211","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Control and Optimization, 2006, 45 (1), pp.26-50. &#x27E8;10.1137/050628982&#x27E9;","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.800000011920929,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W155342407","https://openalex.org/W621523870","https://openalex.org/W1579645751","https://openalex.org/W1968010891","https://openalex.org/W1971650550","https://openalex.org/W1999900551","https://openalex.org/W2002569975","https://openalex.org/W2007954101","https://openalex.org/W2059827058","https://openalex.org/W2067275579","https://openalex.org/W2078172548","https://openalex.org/W2098557421","https://openalex.org/W2099455475","https://openalex.org/W2100486700","https://openalex.org/W2102040002","https://openalex.org/W2108658050","https://openalex.org/W2123353000","https://openalex.org/W2125131148","https://openalex.org/W2134046186","https://openalex.org/W2143415577","https://openalex.org/W2143987183","https://openalex.org/W2151177951","https://openalex.org/W2154482807","https://openalex.org/W2178134361","https://openalex.org/W2303550677","https://openalex.org/W2319479038","https://openalex.org/W2464364536","https://openalex.org/W2796471654","https://openalex.org/W2805848106","https://openalex.org/W2959694995","https://openalex.org/W2986629677"],"related_works":["https://openalex.org/W2054831413","https://openalex.org/W1999673819","https://openalex.org/W3209184047","https://openalex.org/W2026024153","https://openalex.org/W1942635442","https://openalex.org/W4237454804","https://openalex.org/W1990421243","https://openalex.org/W2170835896","https://openalex.org/W2110547027","https://openalex.org/W2539338955"],"abstract_inverted_index":{"Abstract.":[0],"The":[1,13],"classical":[2],"study":[3],"of":[4,6,21,29,40,48,51,70],"controllability":[5,52],"linear":[7,63],"systems":[8],"assumes":[9],"unconstrained":[10],"control":[11,58,69,80],"inputs.":[12],"\u201cdistance":[14],"to":[15,25,53],"uncontrollability":[16],"\u201d":[17],"measures":[18],"the":[19,22,26,30,45,54,57,68,75,79],"size":[20],"smallest":[23],"perturbation":[24],"ma-trix":[27],"description":[28],"system":[31,41],"rendering":[32],"it":[33],"uncontrollable":[34],"and":[35],"is":[36],"a":[37,85],"key":[38],"measure":[39,50],"robustness.":[42],"We":[43],"extend":[44],"standard":[46],"theory":[47],"this":[49],"case":[55,77],"where":[56,78],"input":[59,81],"must":[60],"satisfy":[61],"given":[62,86],"inequalities.":[64],"Specifically,":[65],"we":[66],"consider":[67],"differential":[71],"inclusions,":[72],"concentrating":[73],"on":[74],"particular":[76],"takes":[82],"values":[83],"in":[84],"convex":[87],"cone.":[88]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":7}],"updated_date":"2026-07-17T09:13:05.818461","created_date":"2025-10-10T00:00:00"}
