{"id":"https://openalex.org/W2057237107","doi":"https://doi.org/10.1109/cdc.2011.6160222","title":"Stabilizability of constrained uncertain linear systems via smooth control Lyapunov R-functions","display_name":"Stabilizability of constrained uncertain linear systems via smooth control Lyapunov R-functions","publication_year":2011,"publication_date":"2011-12-01","ids":{"openalex":"https://openalex.org/W2057237107","doi":"https://doi.org/10.1109/cdc.2011.6160222","mag":"2057237107"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2011.6160222","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2011.6160222","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/A5108444192","display_name":"Aldo Balestrino","orcid":null},"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":true,"raw_author_name":"Aldo Balestrino","raw_affiliation_strings":["Department of Energy and Systems Engineering, University of Pisa, Pisa, Italy","Department of Energy and Systems Engineering, University of Pisa, Largo Lazzarino 1, 56122 (Italy)"],"affiliations":[{"raw_affiliation_string":"Department of Energy and Systems Engineering, University of Pisa, Pisa, Italy","institution_ids":["https://openalex.org/I108290504"]},{"raw_affiliation_string":"Department of Energy and Systems Engineering, University of Pisa, Largo Lazzarino 1, 56122 (Italy)","institution_ids":["https://openalex.org/I108290504"]}]},{"author_position":"middle","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 Energy and Systems Engineering, University of Pisa, Pisa, Italy","Department of Energy and Systems Engineering, University of Pisa, Largo Lazzarino 1, 56122 (Italy)"],"affiliations":[{"raw_affiliation_string":"Department of Energy and Systems Engineering, University of Pisa, Pisa, Italy","institution_ids":["https://openalex.org/I108290504"]},{"raw_affiliation_string":"Department of Energy and Systems Engineering, University of Pisa, Largo Lazzarino 1, 56122 (Italy)","institution_ids":["https://openalex.org/I108290504"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5006692330","display_name":"Sergio Grammatico","orcid":"https://orcid.org/0000-0002-6021-2350"},"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":"Sergio Grammatico","raw_affiliation_strings":["Department of Energy and Systems Engineering, University of Pisa, Pisa, Italy","Department of Energy and Systems Engineering, University of Pisa, Largo Lazzarino 1, 56122 (Italy)"],"affiliations":[{"raw_affiliation_string":"Department of Energy and Systems Engineering, University of Pisa, Pisa, Italy","institution_ids":["https://openalex.org/I108290504"]},{"raw_affiliation_string":"Department of Energy and Systems Engineering, University of Pisa, Largo Lazzarino 1, 56122 (Italy)","institution_ids":["https://openalex.org/I108290504"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5108444192"],"corresponding_institution_ids":["https://openalex.org/I108290504"],"apc_list":null,"apc_paid":null,"fwci":3.2626,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.92269574,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"124","issue":null,"first_page":"8182","last_page":"8187"},"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":0.9998999834060669,"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":0.9998999834060669,"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/T10791","display_name":"Advanced Control Systems Optimization","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/T11236","display_name":"Control Systems and Identification","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"}}],"keywords":[{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.7259355783462524},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6916287541389465},{"id":"https://openalex.org/keywords/lyapunov-equation","display_name":"Lyapunov equation","score":0.5496901869773865},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.539408802986145},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.508906364440918},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.5000391006469727},{"id":"https://openalex.org/keywords/smoothing","display_name":"Smoothing","score":0.495388388633728},{"id":"https://openalex.org/keywords/almost-everywhere","display_name":"Almost everywhere","score":0.4687733054161072},{"id":"https://openalex.org/keywords/control-lyapunov-function","display_name":"Control-Lyapunov function","score":0.44406843185424805},{"id":"https://openalex.org/keywords/lyapunov-redesign","display_name":"Lyapunov redesign","score":0.4393956661224365},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.35862985253334045},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2171335220336914},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.18184933066368103},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.17349159717559814},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.1352536976337433}],"concepts":[{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.7259355783462524},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6916287541389465},{"id":"https://openalex.org/C25854792","wikidata":"https://www.wikidata.org/wiki/Q1028945","display_name":"Lyapunov equation","level":4,"score":0.5496901869773865},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.539408802986145},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.508906364440918},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5000391006469727},{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.495388388633728},{"id":"https://openalex.org/C27142425","wikidata":"https://www.wikidata.org/wiki/Q1139334","display_name":"Almost everywhere","level":2,"score":0.4687733054161072},{"id":"https://openalex.org/C201030206","wikidata":"https://www.wikidata.org/wiki/Q5165805","display_name":"Control-Lyapunov function","level":5,"score":0.44406843185424805},{"id":"https://openalex.org/C37935115","wikidata":"https://www.wikidata.org/wiki/Q6707085","display_name":"Lyapunov redesign","level":4,"score":0.4393956661224365},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.35862985253334045},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2171335220336914},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.18184933066368103},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.17349159717559814},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.1352536976337433},{"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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/cdc.2011.6160222","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2011.6160222","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"},{"id":"pmh:oai:arpi.unipi.it:11568/533143","is_oa":false,"landing_page_url":"http://hdl.handle.net/11568/533143","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/conferenceObject"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W1524955749","https://openalex.org/W1525091166","https://openalex.org/W1969144114","https://openalex.org/W1973273925","https://openalex.org/W1983533277","https://openalex.org/W2025135845","https://openalex.org/W2026727219","https://openalex.org/W2036646717","https://openalex.org/W2057541071","https://openalex.org/W2067459192","https://openalex.org/W2068617307","https://openalex.org/W2076634083","https://openalex.org/W2089106311","https://openalex.org/W2104244890","https://openalex.org/W2120207446","https://openalex.org/W2137154260","https://openalex.org/W2171505650","https://openalex.org/W2562009545","https://openalex.org/W2734465626","https://openalex.org/W4298206858","https://openalex.org/W6631316631","https://openalex.org/W6642542322","https://openalex.org/W6669673427"],"related_works":["https://openalex.org/W2349796700","https://openalex.org/W2383986032","https://openalex.org/W3217133416","https://openalex.org/W2358066536","https://openalex.org/W1970635650","https://openalex.org/W2496188264","https://openalex.org/W2126112326","https://openalex.org/W2091455539","https://openalex.org/W2333471870","https://openalex.org/W2374426356"],"abstract_inverted_index":{"The":[0,30,64],"stabilization":[1],"problem":[2],"of":[3,13,28,33,55,66],"constrained":[4],"uncertain":[5],"linear":[6],"systems":[7],"is":[8,62,70,87],"addressed":[9],"via":[10],"the":[11,21,34,52,56,67,72,107],"class":[12],"control":[14,37,102,108],"Lyapunov":[15,38,50,103],"R-functions":[16],"that":[17,71],"are":[18,76],"obtained":[19],"reformulating":[20],"classic":[22],"geometric":[23],"intersection":[24],"operator":[25],"in":[26,112],"terms":[27],"R-functions.":[29],"feasibility":[31],"test":[32],"proposed":[35,68],"smooth":[36,77,96],"functions":[39,104],"can":[40,79,92],"be":[41,80,93],"casted":[42],"into":[43],"(bi)linear":[44],"matrix":[45],"inequalities":[46],"conditions.":[47],"Like":[48],"polyhedral":[49,98],"functions,":[51],"maximal":[53],"estimate":[54],"controlled":[57],"invariant":[58],"state":[59],"space":[60],"set":[61],"achieved.":[63],"advantage":[65],"approach":[69],"inner":[73],"sublevel":[74],"sets":[75],"and":[78,90,99],"made":[81],"everywhere":[82],"differentiable.":[83],"This":[84],"smoothing":[85],"technique":[86],"very":[88],"general":[89],"it":[91],"used":[94],"to":[95,105],"both":[97],"truncated":[100],"ellipsoidal":[101],"improve":[106],"performances,":[109],"as":[110],"shown":[111],"some":[113],"benchmark":[114],"examples.":[115]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}