{"id":"https://openalex.org/W2095167294","doi":"https://doi.org/10.1109/cdc.2011.6161012","title":"Static nonsmooth control Lyapunov function design via dynamic extension","display_name":"Static nonsmooth control Lyapunov function design via dynamic extension","publication_year":2011,"publication_date":"2011-12-01","ids":{"openalex":"https://openalex.org/W2095167294","doi":"https://doi.org/10.1109/cdc.2011.6161012","mag":"2095167294"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2011.6161012","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2011.6161012","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Conference on Decision and Control and European 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/A5067979427","display_name":"Takahiro Yamazaki","orcid":"https://orcid.org/0000-0002-4193-2221"},"institutions":[{"id":"https://openalex.org/I205349734","display_name":"Hokkaido University","ror":"https://ror.org/02e16g702","country_code":"JP","type":"education","lineage":["https://openalex.org/I205349734"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Takahiro Yamazaki","raw_affiliation_strings":["Graduate School of Information Science and Technology, Hokkaido University, Sapporo, Japan","Graduate School of Information Science and Technology, Hokkaido University, Kita-ku N14W8, Sapporo 060-0814, Japan"],"affiliations":[{"raw_affiliation_string":"Graduate School of Information Science and Technology, Hokkaido University, Sapporo, Japan","institution_ids":["https://openalex.org/I205349734"]},{"raw_affiliation_string":"Graduate School of Information Science and Technology, Hokkaido University, Kita-ku N14W8, Sapporo 060-0814, Japan","institution_ids":["https://openalex.org/I205349734"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054322992","display_name":"Yuh Yamashita","orcid":"https://orcid.org/0000-0001-7190-6609"},"institutions":[{"id":"https://openalex.org/I205349734","display_name":"Hokkaido University","ror":"https://ror.org/02e16g702","country_code":"JP","type":"education","lineage":["https://openalex.org/I205349734"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Yuh Yamashita","raw_affiliation_strings":["Graduate School of Information Science and Technology, Hokkaido University, Sapporo, Japan","Graduate School of Information Science and Technology, Hokkaido University, Kita-ku N14W8, Sapporo 060-0814, Japan"],"affiliations":[{"raw_affiliation_string":"Graduate School of Information Science and Technology, Hokkaido University, Sapporo, Japan","institution_ids":["https://openalex.org/I205349734"]},{"raw_affiliation_string":"Graduate School of Information Science and Technology, Hokkaido University, Kita-ku N14W8, Sapporo 060-0814, Japan","institution_ids":["https://openalex.org/I205349734"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5081409402","display_name":"Hisakazu Nakamura","orcid":"https://orcid.org/0000-0002-7683-8761"},"institutions":[{"id":"https://openalex.org/I161296585","display_name":"Tokyo University of Science","ror":"https://ror.org/05sj3n476","country_code":"JP","type":"education","lineage":["https://openalex.org/I161296585"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Hisakazu Nakamura","raw_affiliation_strings":["Tokyo Rika Daigaku, Shinjuku-ku, Tokyo, JP","Department of Electrical Engineering, Faculty of Science and Technology, Tokyo University of Science, Yamazaki 2641, Noda, Chiba 278-8510, Japan"],"affiliations":[{"raw_affiliation_string":"Tokyo Rika Daigaku, Shinjuku-ku, Tokyo, JP","institution_ids":["https://openalex.org/I161296585"]},{"raw_affiliation_string":"Department of Electrical Engineering, Faculty of Science and Technology, Tokyo University of Science, Yamazaki 2641, Noda, Chiba 278-8510, Japan","institution_ids":["https://openalex.org/I161296585"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5067979427"],"corresponding_institution_ids":["https://openalex.org/I205349734"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.13283974,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"7573","last_page":"7578"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.9994999766349792,"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/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.9994999766349792,"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/T10040","display_name":"Adaptive Control of Nonlinear Systems","score":0.9988999962806702,"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/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.9987999796867371,"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/control-theory","display_name":"Control theory (sociology)","score":0.7682133913040161},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.6389428377151489},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.5843895673751831},{"id":"https://openalex.org/keywords/state-space","display_name":"State space","score":0.5570646524429321},{"id":"https://openalex.org/keywords/control-lyapunov-function","display_name":"Control-Lyapunov function","score":0.539397656917572},{"id":"https://openalex.org/keywords/controller","display_name":"Controller (irrigation)","score":0.5317961573600769},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.4996786117553711},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.4623945951461792},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4489981234073639},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4485798478126526},{"id":"https://openalex.org/keywords/constructive","display_name":"Constructive","score":0.4396035671234131},{"id":"https://openalex.org/keywords/lyapunov-redesign","display_name":"Lyapunov redesign","score":0.3012459874153137},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.2165766954421997},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.1429060697555542},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.06236061453819275}],"concepts":[{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.7682133913040161},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.6389428377151489},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.5843895673751831},{"id":"https://openalex.org/C72434380","wikidata":"https://www.wikidata.org/wiki/Q230930","display_name":"State space","level":2,"score":0.5570646524429321},{"id":"https://openalex.org/C201030206","wikidata":"https://www.wikidata.org/wiki/Q5165805","display_name":"Control-Lyapunov function","level":5,"score":0.539397656917572},{"id":"https://openalex.org/C203479927","wikidata":"https://www.wikidata.org/wiki/Q5165939","display_name":"Controller (irrigation)","level":2,"score":0.5317961573600769},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.4996786117553711},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.4623945951461792},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4489981234073639},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4485798478126526},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.4396035671234131},{"id":"https://openalex.org/C37935115","wikidata":"https://www.wikidata.org/wiki/Q6707085","display_name":"Lyapunov redesign","level":4,"score":0.3012459874153137},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.2165766954421997},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.1429060697555542},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.06236061453819275},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","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/C6557445","wikidata":"https://www.wikidata.org/wiki/Q173113","display_name":"Agronomy","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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cdc.2011.6161012","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2011.6161012","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Conference on Decision and Control and European Control Conference","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","score":0.8199999928474426,"id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W178292676","https://openalex.org/W1484739396","https://openalex.org/W1494380031","https://openalex.org/W1965438480","https://openalex.org/W1965796511","https://openalex.org/W1966186934","https://openalex.org/W2041076275","https://openalex.org/W2043930951","https://openalex.org/W2047949777","https://openalex.org/W2066807940","https://openalex.org/W2119130475","https://openalex.org/W2152112251","https://openalex.org/W2154930603","https://openalex.org/W2167943585","https://openalex.org/W2329626928","https://openalex.org/W6607233217","https://openalex.org/W6661737889","https://openalex.org/W6662579094"],"related_works":["https://openalex.org/W3217133416","https://openalex.org/W2349796700","https://openalex.org/W1970635650","https://openalex.org/W2475132469","https://openalex.org/W2383986032","https://openalex.org/W2126112326","https://openalex.org/W2358066536","https://openalex.org/W1976574339","https://openalex.org/W2496188264","https://openalex.org/W2147929414"],"abstract_inverted_index":{"In":[0,78],"this":[1,79],"paper,":[2,80],"we":[3,46,81],"propose":[4],"a":[5,9,18,25,50,55,59,64,68,84,95,113],"method":[6,62,122,168],"to":[7],"obtain":[8],"control":[10,52],"Lyapunov":[11],"function":[12],"(CLF)":[13],"by":[14,171],"the":[15,40,105,108,117,130,139,149,153,166],"reduction":[16],"of":[17,20,39,104,129,165],"CLF":[19,85,106,115,141,151],"an":[21,90,127,172],"augmented":[22],"system":[23],"with":[24,94],"dynamic":[26,32,56,69,96],"compensator.":[27,57],"For":[28],"asymptotically":[29],"stabilizing":[30,51],"control,":[31],"compensators":[33],"are":[34],"not":[35],"necessary":[36],"in":[37,43,76],"most":[38],"cases.":[41],"However,":[42],"some":[44],"cases,":[45],"can":[47,123],"easily":[48],"design":[49,61],"law":[53],"using":[54,63],"Therefore,":[58],"constructive":[60],"static":[65],"controller":[66,70],"via":[67],"has":[71,86],"advantages":[72],"and":[73,98,145,160],"is":[74,157,169],"preferable":[75],"practice.":[77],"assume":[82],"that":[83,100,138],"been":[87],"designed":[88],"on":[89,107,116,152],"extended":[91,109,154],"state":[92,110,119,155],"space":[93,111,156],"compensator,":[97],"show":[99,137],"taking":[101],"minimum":[102,131],"values":[103],"gives":[112],"nonsmooth":[114],"original":[118,150],"space.":[120],"This":[121],"be":[124],"considered":[125],"as":[126],"extension":[128],"projection":[132],"method[1],":[133],"[2].":[134],"We":[135],"also":[136],"obtained":[140],"fulfills":[142],"Lipschitz":[143,158],"continuity":[144],"local":[146],"semiconcavity":[147],"if":[148],"continuous":[159],"locally":[161],"semiconcave.":[162],"The":[163],"effectiveness":[164],"proposed":[167],"demonstrated":[170],"example.":[173]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}