{"id":"https://openalex.org/W2784231638","doi":"https://doi.org/10.1109/cdc.2017.8264471","title":"Smooth Lyapunov functions for multistable hybrid systems on manifolds","display_name":"Smooth Lyapunov functions for multistable hybrid systems on manifolds","publication_year":2017,"publication_date":"2017-12-01","ids":{"openalex":"https://openalex.org/W2784231638","doi":"https://doi.org/10.1109/cdc.2017.8264471","mag":"2784231638"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2017.8264471","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2017.8264471","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2017 IEEE 56th Annual Conference on Decision and Control (CDC)","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/A5041118568","display_name":"Paolo Forni","orcid":"https://orcid.org/0000-0002-5777-8521"},"institutions":[{"id":"https://openalex.org/I47508984","display_name":"Imperial College London","ror":"https://ror.org/041kmwe10","country_code":"GB","type":"education","lineage":["https://openalex.org/I47508984"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Paolo Forni","raw_affiliation_strings":["Dept. of Electrical and Electronic Engineering, Imperial College London, U.K"],"affiliations":[{"raw_affiliation_string":"Dept. of Electrical and Electronic Engineering, Imperial College London, U.K","institution_ids":["https://openalex.org/I47508984"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5037354850","display_name":"David Angeli","orcid":"https://orcid.org/0000-0002-5311-4306"},"institutions":[{"id":"https://openalex.org/I45084792","display_name":"University of Florence","ror":"https://ror.org/04jr1s763","country_code":"IT","type":"education","lineage":["https://openalex.org/I45084792"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"David Angeli","raw_affiliation_strings":["Dept. of Information Engineering, University of Florence, Italy"],"affiliations":[{"raw_affiliation_string":"Dept. of Information Engineering, University of Florence, Italy","institution_ids":["https://openalex.org/I45084792"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5041118568"],"corresponding_institution_ids":["https://openalex.org/I47508984"],"apc_list":null,"apc_paid":null,"fwci":0.4078,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.66209927,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"5481","last_page":"5486"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9990000128746033,"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9990000128746033,"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/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/2739","display_name":"Public Health, Environmental and Occupational Health"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.9835000038146973,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/multistability","display_name":"Multistability","score":0.8524558544158936},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.6381852626800537},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6341351866722107},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.6159001588821411},{"id":"https://openalex.org/keywords/exponential-stability","display_name":"Exponential stability","score":0.568953812122345},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.5020246505737305},{"id":"https://openalex.org/keywords/lyapunov-exponent","display_name":"Lyapunov exponent","score":0.4596211016178131},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4369608163833618},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4169141948223114},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.39521145820617676},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.38548514246940613},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.3660595417022705},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.35729900002479553},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.19146212935447693},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.13916829228401184},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.10486859083175659},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10192239284515381},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.06999248266220093}],"concepts":[{"id":"https://openalex.org/C2776966350","wikidata":"https://www.wikidata.org/wiki/Q6935096","display_name":"Multistability","level":3,"score":0.8524558544158936},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.6381852626800537},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6341351866722107},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.6159001588821411},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.568953812122345},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5020246505737305},{"id":"https://openalex.org/C191544260","wikidata":"https://www.wikidata.org/wiki/Q1238630","display_name":"Lyapunov exponent","level":3,"score":0.4596211016178131},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4369608163833618},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4169141948223114},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.39521145820617676},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.38548514246940613},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3660595417022705},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.35729900002479553},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.19146212935447693},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.13916829228401184},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.10486859083175659},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10192239284515381},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.06999248266220093},{"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/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","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/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/cdc.2017.8264471","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2017.8264471","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2017 IEEE 56th Annual Conference on Decision and Control (CDC)","raw_type":"proceedings-article"},{"id":"pmh:oai:flore.unifi.it:2158/1153391","is_oa":false,"landing_page_url":"http://hdl.handle.net/2158/1153391","pdf_url":null,"source":{"id":"https://openalex.org/S4306402033","display_name":"Florence Research (University of Florence)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I45084792","host_organization_name":"University of Florence","host_organization_lineage":["https://openalex.org/I45084792"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/conferenceObject"},{"id":"pmh:oai:spiral.imperial.ac.uk:10044/1/62226","is_oa":false,"landing_page_url":"http://hdl.handle.net/10044/1/62226","pdf_url":null,"source":{"id":"https://openalex.org/S4306401396","display_name":"Spiral (Imperial College London)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I47508984","host_organization_name":"Imperial College London","host_organization_lineage":["https://openalex.org/I47508984"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE 56th Annual Conference on Decision and Control (CDC)","raw_type":"Conference Paper"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W351069376","https://openalex.org/W1989230227","https://openalex.org/W1994795948","https://openalex.org/W2024582624","https://openalex.org/W2045938917","https://openalex.org/W2052123991","https://openalex.org/W2054136677","https://openalex.org/W2057820893","https://openalex.org/W2058765561","https://openalex.org/W2081779653","https://openalex.org/W2099308299","https://openalex.org/W2112248103","https://openalex.org/W2151136609","https://openalex.org/W2154493443","https://openalex.org/W2162807113","https://openalex.org/W2314410691","https://openalex.org/W2319976289","https://openalex.org/W3138246992","https://openalex.org/W3163755257","https://openalex.org/W4220669412","https://openalex.org/W4252120783","https://openalex.org/W6796125016","https://openalex.org/W6809376820"],"related_works":["https://openalex.org/W4226329279","https://openalex.org/W1527571384","https://openalex.org/W2383189914","https://openalex.org/W3118264548","https://openalex.org/W1979419366","https://openalex.org/W1983507234","https://openalex.org/W2164703465","https://openalex.org/W2168383058","https://openalex.org/W2143247663","https://openalex.org/W2050693590"],"abstract_inverted_index":{"For":[0],"a":[1,22,31],"broad":[2],"class":[3],"of":[4,24,30,34,61,66],"complete":[5],"hybrid":[6],"systems":[7],"evolving":[8],"on":[9,17,27],"Riemannian":[10],"manifolds":[11],"and":[12,38,70],"satisfying":[13],"mild":[14],"regularity":[15],"conditions":[16],"the":[18,28,47],"data":[19],"we":[20],"introduce":[21],"notion":[23,43],"multistability":[25],"based":[26],"existence":[29,65],"finite":[32],"number":[33],"compact,":[35],"globally":[36],"attractive,":[37],"weakly":[39],"invariant":[40],"sets.":[41],"Such":[42],"not":[44],"only":[45],"generalizes":[46],"standard":[48],"global":[49],"uniform":[50],"asymptotic":[51,63],"stability":[52],"requirement,":[53],"but":[54],"can":[55],"also":[56],"be":[57],"characterized":[58],"in":[59],"terms":[60],"equivalent":[62],"properties,":[64],"smooth":[67],"Lyapunov":[68],"functions,":[69],"intrinsic":[71],"robustness":[72],"to":[73],"small":[74],"perturbations.":[75]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
