{"id":"https://openalex.org/W2576550587","doi":"https://doi.org/10.1109/ecc.2016.7810345","title":"Analysis of almost-everywhere stability of a class of discontinuous systems via Lyapunov densities","display_name":"Analysis of almost-everywhere stability of a class of discontinuous systems via Lyapunov densities","publication_year":2016,"publication_date":"2016-06-01","ids":{"openalex":"https://openalex.org/W2576550587","doi":"https://doi.org/10.1109/ecc.2016.7810345","mag":"2576550587"},"language":"en","primary_location":{"id":"doi:10.1109/ecc.2016.7810345","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ecc.2016.7810345","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2016 European Control Conference (ECC)","raw_type":"proceedings-article"},"type":"conference-paper","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/A5077788540","display_name":"Izumi Masubuchi","orcid":"https://orcid.org/0000-0003-1659-5136"},"institutions":[{"id":"https://openalex.org/I65837984","display_name":"Kobe University","ror":"https://ror.org/03tgsfw79","country_code":"JP","type":"education","lineage":["https://openalex.org/I65837984"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Izumi Masubuchi","raw_affiliation_strings":["Graduate School of System Informatics, Kobe University, Nada, Kobe, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Graduate School of System Informatics, Kobe University, Nada, Kobe, Japan","institution_ids":["https://openalex.org/I65837984"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100884201","display_name":"Yuzo Ohta","orcid":null},"institutions":[{"id":"https://openalex.org/I65837984","display_name":"Kobe University","ror":"https://ror.org/03tgsfw79","country_code":"JP","type":"education","lineage":["https://openalex.org/I65837984"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Yuzo Ohta","raw_affiliation_strings":["Graduate School of System Informatics, Kobe University, Nada, Kobe, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Graduate School of System Informatics, Kobe University, Nada, Kobe, Japan","institution_ids":["https://openalex.org/I65837984"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I65837984"],"apc_list":null,"apc_paid":null,"fwci":3.0826,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.92653184,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"567","last_page":"574"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10040","display_name":"Adaptive Control of Nonlinear Systems","score":0.9987000226974487,"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/T10040","display_name":"Adaptive Control of Nonlinear Systems","score":0.9987000226974487,"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":0.9962999820709229,"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9958000183105469,"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/vector-field","display_name":"Vector field","score":0.8000267148017883},{"id":"https://openalex.org/keywords/discontinuity","display_name":"Discontinuity (linguistics)","score":0.7306321859359741},{"id":"https://openalex.org/keywords/almost-everywhere","display_name":"Almost everywhere","score":0.6715257167816162},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6583287119865417},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.6470434665679932},{"id":"https://openalex.org/keywords/smoothness","display_name":"Smoothness","score":0.6242693662643433},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.5782651305198669},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5575923919677734},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.5548268556594849},{"id":"https://openalex.org/keywords/lyapunov-exponent","display_name":"Lyapunov exponent","score":0.5345959067344666},{"id":"https://openalex.org/keywords/lyapunov-redesign","display_name":"Lyapunov redesign","score":0.48235267400741577},{"id":"https://openalex.org/keywords/lyapunov-equation","display_name":"Lyapunov equation","score":0.4795222580432892},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4755370616912842},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.43853792548179626},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4360659122467041},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.4056053161621094},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1757153570652008},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08979448676109314},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0857485830783844}],"concepts":[{"id":"https://openalex.org/C91188154","wikidata":"https://www.wikidata.org/wiki/Q186247","display_name":"Vector field","level":2,"score":0.8000267148017883},{"id":"https://openalex.org/C2777042112","wikidata":"https://www.wikidata.org/wiki/Q5281658","display_name":"Discontinuity (linguistics)","level":2,"score":0.7306321859359741},{"id":"https://openalex.org/C27142425","wikidata":"https://www.wikidata.org/wiki/Q1139334","display_name":"Almost everywhere","level":2,"score":0.6715257167816162},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6583287119865417},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.6470434665679932},{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.6242693662643433},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.5782651305198669},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5575923919677734},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.5548268556594849},{"id":"https://openalex.org/C191544260","wikidata":"https://www.wikidata.org/wiki/Q1238630","display_name":"Lyapunov exponent","level":3,"score":0.5345959067344666},{"id":"https://openalex.org/C37935115","wikidata":"https://www.wikidata.org/wiki/Q6707085","display_name":"Lyapunov redesign","level":4,"score":0.48235267400741577},{"id":"https://openalex.org/C25854792","wikidata":"https://www.wikidata.org/wiki/Q1028945","display_name":"Lyapunov equation","level":4,"score":0.4795222580432892},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4755370616912842},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.43853792548179626},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4360659122467041},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.4056053161621094},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1757153570652008},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08979448676109314},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0857485830783844},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/ecc.2016.7810345","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ecc.2016.7810345","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2016 European Control Conference (ECC)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2460998745","display_name":"Development of the methodologies for high-performance robust and nonlinear control system design","funder_award_id":"26420418","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"}],"funders":[{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W1729334489","https://openalex.org/W1832389169","https://openalex.org/W1998433615","https://openalex.org/W2045938917","https://openalex.org/W2050383062","https://openalex.org/W2056751949","https://openalex.org/W2096143362","https://openalex.org/W2105355605","https://openalex.org/W2115805176","https://openalex.org/W2130461596","https://openalex.org/W2148780273","https://openalex.org/W2152855691","https://openalex.org/W2154493443","https://openalex.org/W2170665905","https://openalex.org/W2172140892","https://openalex.org/W2493925475","https://openalex.org/W3099133928","https://openalex.org/W4249492311"],"related_works":["https://openalex.org/W2349796700","https://openalex.org/W2284157877","https://openalex.org/W2383986032","https://openalex.org/W1789972284","https://openalex.org/W1983507234","https://openalex.org/W2534107666","https://openalex.org/W1986563546","https://openalex.org/W2780579194","https://openalex.org/W1979419366","https://openalex.org/W2411577087"],"abstract_inverted_index":{"Methods":[0],"of":[1,7,18,24,30,34,43,48,64,67,81,83,98,108,110],"Lyapunov":[2,89],"densities":[3],"for":[4,61],"stability":[5,63],"analysis":[6],"nonlinear":[8,35],"systems":[9,71],"have":[10],"been":[11],"extended":[12],"to":[13,40],"various":[14],"problems":[15],"including":[16],"synthesis":[17],"state":[19],"feedback":[20],"gains.":[21],"However,":[22],"most":[23],"the":[25,31,46,49,84,95,99,106,111],"existing":[26],"results":[27],"assume":[28],"smoothness":[29],"vector":[32,100,112],"field":[33],"systems,":[36],"which":[37],"is":[38],"essential":[39],"utilize":[41],"derivative":[42,93],"measures":[44],"along":[45],"trajectories":[47],"system.":[50],"Unlike":[51],"such":[52],"previous":[53],"results,":[54],"this":[55],"paper":[56],"provides":[57],"a":[58,65,88,103],"Lyapunov-density":[59],"condition":[60,79,104],"almost-everywhere":[62],"class":[66],"piecewise":[68],"smooth":[69],"discontinuous":[70],"under":[72],"some":[73],"assumptions":[74],"on":[75,94,105],"well-posedness.":[76],"The":[77],"proposed":[78],"consists":[80],"positivity":[82],"measure":[85],"given":[86],"by":[87],"density":[90],"and":[91,102],"its":[92],"differentiable":[96],"points":[97],"fields":[101],"surfaces":[107],"discontinuity":[109],"field.":[113]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}
