{"id":"https://openalex.org/W2491799359","doi":"https://doi.org/10.1109/acc.2016.7524925","title":"Positivity conditions of Lyapunov functions for systems with slope restricted nonlinearities","display_name":"Positivity conditions of Lyapunov functions for systems with slope restricted nonlinearities","publication_year":2016,"publication_date":"2016-07-01","ids":{"openalex":"https://openalex.org/W2491799359","doi":"https://doi.org/10.1109/acc.2016.7524925","mag":"2491799359"},"language":"en","primary_location":{"id":"doi:10.1109/acc.2016.7524925","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2016.7524925","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2016 American Control Conference (ACC)","raw_type":"proceedings-article"},"type":"preprint","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hal.science/hal-01710297","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5066966226","display_name":"Gi\u00f3rgio Valm\u00f3rbida","orcid":"https://orcid.org/0000-0002-1710-8590"},"institutions":[{"id":"https://openalex.org/I4210097418","display_name":"Laboratoire des signaux et syst\u00e8mes","ror":"https://ror.org/00skw9v43","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I277688954","https://openalex.org/I277688954","https://openalex.org/I4210097418","https://openalex.org/I4210107720"]},{"id":"https://openalex.org/I277688954","display_name":"Universit\u00e9 Paris-Saclay","ror":"https://ror.org/03xjwb503","country_code":"FR","type":"education","lineage":["https://openalex.org/I277688954"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1294671590"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"G. Valmorbida","raw_affiliation_strings":["CNRS, Universit\u00e9 Paris-Saclay, Gif-sur-Yvette, France","L2S - Laboratoire des signaux et syst\u00e8mes (Plateau de Moulon 3 rue Joliot Curie 91192 GIF SUR YVETTE CEDEX - France)"],"affiliations":[{"raw_affiliation_string":"CNRS, Universit\u00e9 Paris-Saclay, Gif-sur-Yvette, France","institution_ids":["https://openalex.org/I277688954","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"L2S - Laboratoire des signaux et syst\u00e8mes (Plateau de Moulon 3 rue Joliot Curie 91192 GIF SUR YVETTE CEDEX - France)","institution_ids":["https://openalex.org/I4210097418"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5064818238","display_name":"Ross Drummond","orcid":"https://orcid.org/0000-0002-2586-1718"},"institutions":[{"id":"https://openalex.org/I2802123492","display_name":"Oxford Research Group","ror":"https://ror.org/00z4w4f29","country_code":"GB","type":"nonprofit","lineage":["https://openalex.org/I2802123492"]},{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]},{"id":"https://openalex.org/I4210146410","display_name":"Science Oxford","ror":"https://ror.org/04j8yhy50","country_code":"GB","type":"nonprofit","lineage":["https://openalex.org/I4210146410"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"R. Drummond","raw_affiliation_strings":["Control Group, University of Oxford, Oxford, United Kingdom","Department of Engineering Science (Department of Engineering Science University of Oxford Parks Road OXFORD OX1 3PJ UK - United Kingdom)"],"affiliations":[{"raw_affiliation_string":"Control Group, University of Oxford, Oxford, United Kingdom","institution_ids":["https://openalex.org/I2802123492","https://openalex.org/I40120149"]},{"raw_affiliation_string":"Department of Engineering Science (Department of Engineering Science University of Oxford Parks Road OXFORD OX1 3PJ UK - United Kingdom)","institution_ids":["https://openalex.org/I4210146410","https://openalex.org/I40120149"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5038299471","display_name":"Stephen Duncan","orcid":"https://orcid.org/0000-0002-9525-7305"},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]},{"id":"https://openalex.org/I2802123492","display_name":"Oxford Research Group","ror":"https://ror.org/00z4w4f29","country_code":"GB","type":"nonprofit","lineage":["https://openalex.org/I2802123492"]},{"id":"https://openalex.org/I4210146410","display_name":"Science Oxford","ror":"https://ror.org/04j8yhy50","country_code":"GB","type":"nonprofit","lineage":["https://openalex.org/I4210146410"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"S. R. Duncan","raw_affiliation_strings":["Control Group, University of Oxford, Oxford, United Kingdom","Department of Engineering Science (Department of Engineering Science University of Oxford Parks Road OXFORD OX1 3PJ UK - United Kingdom)"],"affiliations":[{"raw_affiliation_string":"Control Group, University of Oxford, Oxford, United Kingdom","institution_ids":["https://openalex.org/I2802123492","https://openalex.org/I40120149"]},{"raw_affiliation_string":"Department of Engineering Science (Department of Engineering Science University of Oxford Parks Road OXFORD OX1 3PJ UK - United Kingdom)","institution_ids":["https://openalex.org/I4210146410","https://openalex.org/I40120149"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5066966226"],"corresponding_institution_ids":["https://openalex.org/I4210097418","https://openalex.org/I277688954","https://openalex.org/I1294671590"],"apc_list":null,"apc_paid":null,"fwci":2.41549546,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.90820721,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"3","issue":null,"first_page":"258","last_page":"263"},"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":0.9994999766349792,"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":0.9987999796867371,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.8185265064239502},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6696323752403259},{"id":"https://openalex.org/keywords/lyapunov-redesign","display_name":"Lyapunov redesign","score":0.6221506595611572},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6179190874099731},{"id":"https://openalex.org/keywords/lyapunov-equation","display_name":"Lyapunov equation","score":0.6153650879859924},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.6034802794456482},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.580676257610321},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5738246440887451},{"id":"https://openalex.org/keywords/positive-definite-matrix","display_name":"Positive-definite matrix","score":0.5729206800460815},{"id":"https://openalex.org/keywords/lyapunov-exponent","display_name":"Lyapunov exponent","score":0.5620983242988586},{"id":"https://openalex.org/keywords/term","display_name":"Term (time)","score":0.5448321104049683},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.47983381152153015},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.447234183549881},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.44404512643814087},{"id":"https://openalex.org/keywords/sign","display_name":"Sign (mathematics)","score":0.44357430934906006},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.42618727684020996},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.31290942430496216},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.16214656829833984},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08319801092147827}],"concepts":[{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.8185265064239502},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6696323752403259},{"id":"https://openalex.org/C37935115","wikidata":"https://www.wikidata.org/wiki/Q6707085","display_name":"Lyapunov redesign","level":4,"score":0.6221506595611572},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6179190874099731},{"id":"https://openalex.org/C25854792","wikidata":"https://www.wikidata.org/wiki/Q1028945","display_name":"Lyapunov equation","level":4,"score":0.6153650879859924},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.6034802794456482},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.580676257610321},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5738246440887451},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.5729206800460815},{"id":"https://openalex.org/C191544260","wikidata":"https://www.wikidata.org/wiki/Q1238630","display_name":"Lyapunov exponent","level":3,"score":0.5620983242988586},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.5448321104049683},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.47983381152153015},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.447234183549881},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.44404512643814087},{"id":"https://openalex.org/C139676723","wikidata":"https://www.wikidata.org/wiki/Q1193832","display_name":"Sign (mathematics)","level":2,"score":0.44357430934906006},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.42618727684020996},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.31290942430496216},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.16214656829833984},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08319801092147827},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/acc.2016.7524925","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2016.7524925","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2016 American Control Conference (ACC)","raw_type":"proceedings-article"},{"id":"pmh:oai:HAL:hal-01710297v1","is_oa":true,"landing_page_url":"https://hal.science/hal-01710297","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"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":"2016 American Control Conference (ACC)","raw_type":"info:eu-repo/semantics/conferenceObject"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-01710297v1","is_oa":true,"landing_page_url":"https://hal.science/hal-01710297","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"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":"2016 American Control Conference (ACC)","raw_type":"info:eu-repo/semantics/conferenceObject"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities","score":0.4000000059604645}],"awards":[{"id":"https://openalex.org/G6936717642","display_name":null,"funder_award_id":"EP/P005411/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G8029175688","display_name":null,"funder_award_id":"EP/J010537/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W608511283","https://openalex.org/W1968114261","https://openalex.org/W1981166335","https://openalex.org/W1981201107","https://openalex.org/W1994221686","https://openalex.org/W2006736427","https://openalex.org/W2028717619","https://openalex.org/W2063493327","https://openalex.org/W2064486942","https://openalex.org/W2083365871","https://openalex.org/W2097944741","https://openalex.org/W2101787562","https://openalex.org/W2101928099","https://openalex.org/W2147439098","https://openalex.org/W2152421112","https://openalex.org/W2169615838","https://openalex.org/W3210839039","https://openalex.org/W4212991224","https://openalex.org/W4244799121","https://openalex.org/W4302585512","https://openalex.org/W6808208019"],"related_works":["https://openalex.org/W2349796700","https://openalex.org/W2383986032","https://openalex.org/W3194517843","https://openalex.org/W2534107666","https://openalex.org/W1977987201","https://openalex.org/W2374426356","https://openalex.org/W2121515234","https://openalex.org/W2059628530","https://openalex.org/W2496188264","https://openalex.org/W1979419366"],"abstract_inverted_index":{"This":[0,73],"paper":[1,58],"considers":[2],"absolute":[3],"stability":[4,124],"for":[5,69,123,129,134],"Lur'e":[6,91,113],"systems":[7],"consisting":[8],"of":[9,12,33,56,89,108,117],"the":[10,48,51,62,90,106,109,130,135],"interconnection":[11],"a":[13,17,39,43,81,120],"linear":[14],"plant":[15],"with":[16,42,112],"nonlinear":[18],"feedback.":[19],"The":[20,53,115],"nonlinearity":[21],"is":[22,36,59],"assumed":[23],"to":[24,60,77,105],"be":[25,78,103],"both":[26,47,128],"sector":[27],"bounded":[28],"and":[29,50,86,133],"slope":[30],"restricted.":[31],"Stability":[32],"this":[34,57],"system":[35],"determined":[37],"using":[38],"Lyapunov":[40,71,75,121],"function":[41,122],"quadratic":[44,84,110],"term":[45,92],"on":[46],"states":[49],"nonlinearity.":[52],"main":[54],"result":[55],"relax":[61],"positivity":[63],"conditions":[64],"that":[65,99],"have":[66],"been":[67],"imposed":[68],"such":[70,119],"functions.":[72],"allows":[74],"functions":[76],"constructed":[79],"without":[80],"positive":[82],"definite":[83],"matrix":[85],"whose":[87],"scalars":[88],"are":[93,126],"not":[94],"sign-definite.":[95],"We":[96],"also":[97],"show":[98],"previous":[100],"results":[101],"can":[102],"simplified":[104],"case":[107,132],"form":[111],"term.":[114],"benefits":[116],"considering":[118],"analysis":[125],"shown":[127],"global":[131],"local":[136],"case.":[137]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
