{"id":"https://openalex.org/W2049271566","doi":"https://doi.org/10.1109/tac.2013.2281479","title":"Control-Sharing and Merging Control Lyapunov Functions","display_name":"Control-Sharing and Merging Control Lyapunov Functions","publication_year":2013,"publication_date":"2013-09-11","ids":{"openalex":"https://openalex.org/W2049271566","doi":"https://doi.org/10.1109/tac.2013.2281479","mag":"2049271566"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2013.2281479","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2013.2281479","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://ieeexplore.ieee.org/document/6595585","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5006692330","display_name":"Sergio Grammatico","orcid":"https://orcid.org/0000-0002-6021-2350"},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH"],"is_corresponding":true,"raw_author_name":"Sergio Grammatico","raw_affiliation_strings":["ETH Zurich, Automatic Control Laboratory, Zurich, Switzerland","[Autom. Control Lab., ETH Zurich, Z\u00fcrich, Switzerland]"],"affiliations":[{"raw_affiliation_string":"ETH Zurich, Automatic Control Laboratory, Zurich, Switzerland","institution_ids":["https://openalex.org/I35440088"]},{"raw_affiliation_string":"[Autom. Control Lab., ETH Zurich, Z\u00fcrich, Switzerland]","institution_ids":["https://openalex.org/I35440088"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054472321","display_name":"Franco Blanchini","orcid":"https://orcid.org/0000-0002-4109-5531"},"institutions":[{"id":"https://openalex.org/I129043915","display_name":"University of Udine","ror":"https://ror.org/05ht0mh31","country_code":"IT","type":"education","lineage":["https://openalex.org/I129043915"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Franco Blanchini","raw_affiliation_strings":["Department of Mathematics and Informatics, University of Udine, Udine, Italy","Dept. of Math. & Inf., Univ. of Udine, Udine, Italy"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Informatics, University of Udine, Udine, Italy","institution_ids":["https://openalex.org/I129043915"]},{"raw_affiliation_string":"Dept. of Math. & Inf., Univ. of Udine, Udine, Italy","institution_ids":["https://openalex.org/I129043915"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5079569776","display_name":"Andrea Caiti","orcid":"https://orcid.org/0000-0002-5780-3299"},"institutions":[{"id":"https://openalex.org/I108290504","display_name":"University of Pisa","ror":"https://ror.org/03ad39j10","country_code":"IT","type":"education","lineage":["https://openalex.org/I108290504"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Andrea Caiti","raw_affiliation_strings":["Department of Information Engineering, University of Pisa, Pisa, Italy"],"affiliations":[{"raw_affiliation_string":"Department of Information Engineering, University of Pisa, Pisa, Italy","institution_ids":["https://openalex.org/I108290504"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5006692330"],"corresponding_institution_ids":["https://openalex.org/I35440088"],"apc_list":null,"apc_paid":null,"fwci":4.5446,"has_fulltext":false,"cited_by_count":29,"citation_normalized_percentile":{"value":0.94362344,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":93,"max":99},"biblio":{"volume":"59","issue":"1","first_page":"107","last_page":"119"},"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":0.9998000264167786,"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":0.9998000264167786,"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/T12772","display_name":"Control and Stability of Dynamical 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"}},{"id":"https://openalex.org/T10040","display_name":"Adaptive Control of Nonlinear Systems","score":0.9983999729156494,"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/lyapunov-function","display_name":"Lyapunov function","score":0.7087364792823792},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.6367716193199158},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6006640195846558},{"id":"https://openalex.org/keywords/constructive","display_name":"Constructive","score":0.5150213241577148},{"id":"https://openalex.org/keywords/control-lyapunov-function","display_name":"Control-Lyapunov function","score":0.4973662197589874},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.47746825218200684},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.45648619532585144},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4509064257144928},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.4251896142959595},{"id":"https://openalex.org/keywords/lyapunov-redesign","display_name":"Lyapunov redesign","score":0.3819899260997772},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.35523998737335205},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.28523311018943787},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.266485333442688},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.19204330444335938},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.15416407585144043}],"concepts":[{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.7087364792823792},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.6367716193199158},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6006640195846558},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.5150213241577148},{"id":"https://openalex.org/C201030206","wikidata":"https://www.wikidata.org/wiki/Q5165805","display_name":"Control-Lyapunov function","level":5,"score":0.4973662197589874},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.47746825218200684},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.45648619532585144},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4509064257144928},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.4251896142959595},{"id":"https://openalex.org/C37935115","wikidata":"https://www.wikidata.org/wiki/Q6707085","display_name":"Lyapunov redesign","level":4,"score":0.3819899260997772},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.35523998737335205},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.28523311018943787},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.266485333442688},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.19204330444335938},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.15416407585144043},{"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/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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","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":3,"locations":[{"id":"doi:10.1109/tac.2013.2281479","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2013.2281479","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-article"},{"id":"pmh:oai:air.uniud.it:11390/1006946","is_oa":false,"landing_page_url":"http://www.scopus.com/inward/record.url?eid=2-s2.0-84891613968&partnerID=40&md5=4f2ae311f775973ea5eb6eb1b47e3796","pdf_url":null,"source":{"id":"https://openalex.org/S4306401163","display_name":"Institutional Research Information System (University of Udine)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I129043915","host_organization_name":"University of Udine","host_organization_lineage":["https://openalex.org/I129043915"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:arpi.unipi.it:11568/372467","is_oa":true,"landing_page_url":"https://ieeexplore.ieee.org/document/6595585","pdf_url":null,"source":{"id":"https://openalex.org/S4377196265","display_name":"CINECA IRIS Institutial research information system (University of Pisa)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I108290504","host_organization_name":"University of Pisa","host_organization_lineage":["https://openalex.org/I108290504"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:arpi.unipi.it:11568/372467","is_oa":true,"landing_page_url":"https://ieeexplore.ieee.org/document/6595585","pdf_url":null,"source":{"id":"https://openalex.org/S4377196265","display_name":"CINECA IRIS Institutial research information system (University of Pisa)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I108290504","host_organization_name":"University of Pisa","host_organization_lineage":["https://openalex.org/I108290504"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.7300000190734863}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":41,"referenced_works":["https://openalex.org/W83782864","https://openalex.org/W578614108","https://openalex.org/W1484739396","https://openalex.org/W1521510883","https://openalex.org/W1522972598","https://openalex.org/W1593239107","https://openalex.org/W1600295805","https://openalex.org/W1880805667","https://openalex.org/W1969144114","https://openalex.org/W1973273925","https://openalex.org/W1996715315","https://openalex.org/W2008227730","https://openalex.org/W2020998673","https://openalex.org/W2021563297","https://openalex.org/W2023729441","https://openalex.org/W2024217766","https://openalex.org/W2026727219","https://openalex.org/W2057541071","https://openalex.org/W2062646931","https://openalex.org/W2068617307","https://openalex.org/W2076634083","https://openalex.org/W2085985420","https://openalex.org/W2089106311","https://openalex.org/W2093379483","https://openalex.org/W2095589469","https://openalex.org/W2120207446","https://openalex.org/W2137154260","https://openalex.org/W2141560115","https://openalex.org/W2147439098","https://openalex.org/W2149592887","https://openalex.org/W2162193446","https://openalex.org/W2500734973","https://openalex.org/W2734465626","https://openalex.org/W4239216443","https://openalex.org/W4242878961","https://openalex.org/W4249667877","https://openalex.org/W4298206858","https://openalex.org/W6631172057","https://openalex.org/W6635615183","https://openalex.org/W6642542322","https://openalex.org/W6669673427"],"related_works":["https://openalex.org/W2349796700","https://openalex.org/W2475132469","https://openalex.org/W2147929414","https://openalex.org/W1970635650","https://openalex.org/W2383986032","https://openalex.org/W2496188264","https://openalex.org/W2358066536","https://openalex.org/W2126112326","https://openalex.org/W1976574339","https://openalex.org/W2054171707"],"abstract_inverted_index":{"Given":[0],"two":[1,23,44,89,166],"control":[2,78],"Lyapunov":[3,85],"functions":[4,46],"(CLFs),":[5],"a":[6,9,15,76,153],"\u201cmerging\u201d":[7],"is":[8,14,29,99,127,162],"new":[10,35],"CLF":[11],"whose":[12],"gradient":[13],"positive":[16],"combination":[17],"of":[18,21,42,75,87,95,118,123,139],"the":[19,22,43,49,55,69,73,84,88,93,107,115,149,158],"gradients":[20],"parents":[24,45],"CLFs.":[25,97,170],"The":[26,121],"merging":[27,96],"function":[28,36],"an":[30],"important":[31],"trade-off":[32],"since":[33],"this":[34,137],"may,":[37],"for":[38,103],"instance,":[39],"approximate":[40],"one":[41],"close":[47,53],"to":[48,54,147,164],"origin,":[50],"while":[51],"being":[52],"other":[56],"far":[57],"away.":[58],"For":[59,136],"nonlinear":[60],"control-affine":[61],"systems,":[62,106,140],"some":[63],"equivalence":[64,132],"properties":[65],"are":[66,134,145],"shown":[67,100],"between":[68],"control-sharing":[70,108,150],"property,":[71],"i.e.,":[72],"existence":[74,94],"single":[77],"law":[79],"which":[80],"makes":[81],"simultaneously":[82],"negative":[83],"derivatives":[86],"given":[90],"CLFs,":[91],"and":[92,130],"It":[98],"that,":[101],"even":[102],"linear":[104,124,141],"time-invariant":[105],"property":[109],"does":[110],"not":[111],"always":[112],"hold,":[113],"with":[114],"remarkable":[116],"exception":[117],"planar":[119],"systems.":[120],"class":[122,138],"differential":[125],"inclusions":[126],"also":[128],"discussed":[129],"similar":[131],"results":[133],"presented.":[135],"matrix":[142],"inequalities":[143],"conditions":[144],"provided":[146],"guarantee":[148],"property.":[151],"Finally,":[152],"constructive":[154],"procedure,":[155],"based":[156],"on":[157],"recently":[159],"considered":[160],"\u201cR-functions,\u201d":[161],"defined":[163],"merge":[165],"smooth":[167],"positively":[168],"homogeneous":[169]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}