{"id":"https://openalex.org/W1821823409","doi":"https://doi.org/10.23919/ecc.2013.6669684","title":"Incremental stability of planar Filippov systems","display_name":"Incremental stability of planar Filippov systems","publication_year":2013,"publication_date":"2013-07-01","ids":{"openalex":"https://openalex.org/W1821823409","doi":"https://doi.org/10.23919/ecc.2013.6669684","mag":"1821823409"},"language":"en","primary_location":{"id":"doi:10.23919/ecc.2013.6669684","is_oa":false,"landing_page_url":"https://doi.org/10.23919/ecc.2013.6669684","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2013 European Control Conference (ECC)","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/A5034953482","display_name":"Mario di Bernardo","orcid":"https://orcid.org/0000-0002-2171-4745"},"institutions":[{"id":"https://openalex.org/I36234482","display_name":"University of Bristol","ror":"https://ror.org/0524sp257","country_code":"GB","type":"education","lineage":["https://openalex.org/I36234482"]},{"id":"https://openalex.org/I71267560","display_name":"University of Naples Federico II","ror":"https://ror.org/05290cv24","country_code":"IT","type":"education","lineage":["https://openalex.org/I71267560"]}],"countries":["GB","IT"],"is_corresponding":true,"raw_author_name":"Mario di Bernardo","raw_affiliation_strings":["Department of Engineering Mathematics, University of Bristol University, Clifton, Bristol, UK","Department of Systems and Computer Engineering, University of Naples Federico II, Naples, Italy#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Engineering Mathematics, University of Bristol University, Clifton, Bristol, UK","institution_ids":["https://openalex.org/I36234482"]},{"raw_affiliation_string":"Department of Systems and Computer Engineering, University of Naples Federico II, Naples, Italy#TAB#","institution_ids":["https://openalex.org/I71267560"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5061224523","display_name":"Davide Liuzza","orcid":"https://orcid.org/0000-0003-1791-2295"},"institutions":[{"id":"https://openalex.org/I71267560","display_name":"University of Naples Federico II","ror":"https://ror.org/05290cv24","country_code":"IT","type":"education","lineage":["https://openalex.org/I71267560"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Davide Liuzza","raw_affiliation_strings":["Department of Systems and Computer Engineering, University of Naples Federico II, Naples, Italy","Department of Systems and Computer Engineering, University of Naples Federico II, Naples, Italy#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Systems and Computer Engineering, University of Naples Federico II, Naples, Italy","institution_ids":["https://openalex.org/I71267560"]},{"raw_affiliation_string":"Department of Systems and Computer Engineering, University of Naples Federico II, Naples, Italy#TAB#","institution_ids":["https://openalex.org/I71267560"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5034953482"],"corresponding_institution_ids":["https://openalex.org/I36234482","https://openalex.org/I71267560"],"apc_list":null,"apc_paid":null,"fwci":3.5347,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.92118888,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"3706","last_page":"3711"},"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":0.9984999895095825,"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/T12772","display_name":"Control and Stability of Dynamical 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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9962000250816345,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9898999929428101,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/exponential-stability","display_name":"Exponential stability","score":0.687091588973999},{"id":"https://openalex.org/keywords/discontinuity","display_name":"Discontinuity (linguistics)","score":0.6676961183547974},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.6492272615432739},{"id":"https://openalex.org/keywords/differential-inclusion","display_name":"Differential inclusion","score":0.5965373516082764},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5853254795074463},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.5728870630264282},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.49212759733200073},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.47698527574539185},{"id":"https://openalex.org/keywords/contraction","display_name":"Contraction (grammar)","score":0.418901652097702},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.39693397283554077},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.320076584815979},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.26261061429977417},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.19991520047187805},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.1291942298412323},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09802937507629395},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0910508930683136},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.08002659678459167}],"concepts":[{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.687091588973999},{"id":"https://openalex.org/C2777042112","wikidata":"https://www.wikidata.org/wiki/Q5281658","display_name":"Discontinuity (linguistics)","level":2,"score":0.6676961183547974},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.6492272615432739},{"id":"https://openalex.org/C70834904","wikidata":"https://www.wikidata.org/wiki/Q1054638","display_name":"Differential inclusion","level":2,"score":0.5965373516082764},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5853254795074463},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.5728870630264282},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.49212759733200073},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.47698527574539185},{"id":"https://openalex.org/C163415756","wikidata":"https://www.wikidata.org/wiki/Q126473","display_name":"Contraction (grammar)","level":2,"score":0.418901652097702},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.39693397283554077},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.320076584815979},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.26261061429977417},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.19991520047187805},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.1291942298412323},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09802937507629395},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0910508930683136},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.08002659678459167},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0},{"id":"https://openalex.org/C126322002","wikidata":"https://www.wikidata.org/wiki/Q11180","display_name":"Internal medicine","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.23919/ecc.2013.6669684","is_oa":false,"landing_page_url":"https://doi.org/10.23919/ecc.2013.6669684","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2013 European Control Conference (ECC)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W195034729","https://openalex.org/W585465338","https://openalex.org/W1516289514","https://openalex.org/W1537842733","https://openalex.org/W1543420164","https://openalex.org/W1563289057","https://openalex.org/W1581952967","https://openalex.org/W1592648094","https://openalex.org/W1972807647","https://openalex.org/W1977291814","https://openalex.org/W2001069171","https://openalex.org/W2008663032","https://openalex.org/W2014656160","https://openalex.org/W2015745168","https://openalex.org/W2020466691","https://openalex.org/W2029063034","https://openalex.org/W2048723778","https://openalex.org/W2049265628","https://openalex.org/W2064079474","https://openalex.org/W2066323216","https://openalex.org/W2082114857","https://openalex.org/W2117079884","https://openalex.org/W2134889984","https://openalex.org/W2320012146","https://openalex.org/W2322760626"],"related_works":["https://openalex.org/W2152564765","https://openalex.org/W2606062883","https://openalex.org/W4249020370","https://openalex.org/W1557320772","https://openalex.org/W4288351327","https://openalex.org/W2155270558","https://openalex.org/W2198405777","https://openalex.org/W2054897547","https://openalex.org/W2146846916","https://openalex.org/W2777927656"],"abstract_inverted_index":{"We":[0,47],"study":[1],"the":[2,53,57],"problem":[3],"of":[4,8,43,56],"proving":[5],"incremental":[6,40,54],"stability":[7,42,55],"a":[9,31],"planar":[10],"Filippov":[11],"system.":[12,59],"In":[13],"particular,":[14],"referring":[15],"to":[16,38,73],"systems":[17],"that":[18],"present":[19],"an":[20],"attractive":[21],"sliding":[22,44],"region":[23,36],"on":[24,34,64],"their":[25,71],"discontinuity":[26],"boundary,":[27],"we":[28],"will":[29,48],"give":[30],"differential":[32],"condition":[33],"such":[35],"able":[37],"guarantee":[39],"exponential":[41],"mode":[45],"trajectories.":[46],"then":[49],"derive":[50],"conditions":[51],"for":[52],"whole":[58],"The":[60],"approach":[61],"is":[62],"based":[63],"using":[65],"tools":[66],"from":[67],"contraction":[68],"theory,":[69],"extending":[70],"applicability":[72],"include":[74],"discontinuous":[75],"dynamical":[76],"systems.":[77]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}