{"id":"https://openalex.org/W2093545739","doi":"https://doi.org/10.1109/cdc.2011.6161130","title":"A new class of Lyapunov functions for nonstandard switching systems: The stability analysis problem","display_name":"A new class of Lyapunov functions for nonstandard switching systems: The stability analysis problem","publication_year":2011,"publication_date":"2011-12-01","ids":{"openalex":"https://openalex.org/W2093545739","doi":"https://doi.org/10.1109/cdc.2011.6161130","mag":"2093545739"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2011.6161130","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2011.6161130","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":"preprint","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/A5021012069","display_name":"Carlos Alberto Cavichioli Gonzaga","orcid":null},"institutions":[{"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"]},{"id":"https://openalex.org/I4210110792","display_name":"Centre de Recherche en Automatique de Nancy","ror":"https://ror.org/022r5hc56","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I4210099203","https://openalex.org/I4210100260","https://openalex.org/I4210110792","https://openalex.org/I4210159245","https://openalex.org/I90183372"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Carlos A. Cavichioli Gonzaga","raw_affiliation_strings":["CRAN UMR 7039 CNRS, ENSEM, Nancy Universit\u00e8, Vandoeuvre, France"],"affiliations":[{"raw_affiliation_string":"CRAN UMR 7039 CNRS, ENSEM, Nancy Universit\u00e8, Vandoeuvre, France","institution_ids":["https://openalex.org/I4210110792","https://openalex.org/I1294671590"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5002669063","display_name":"Marc Jungers","orcid":"https://orcid.org/0000-0002-6670-3249"},"institutions":[{"id":"https://openalex.org/I4210110792","display_name":"Centre de Recherche en Automatique de Nancy","ror":"https://ror.org/022r5hc56","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I4210099203","https://openalex.org/I4210100260","https://openalex.org/I4210110792","https://openalex.org/I4210159245","https://openalex.org/I90183372"]},{"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":false,"raw_author_name":"Marc Jungers","raw_affiliation_strings":["CRAN UMR 7039 CNRS, ENSEM, Nancy Universit\u00e8, Vandoeuvre, France"],"affiliations":[{"raw_affiliation_string":"CRAN UMR 7039 CNRS, ENSEM, Nancy Universit\u00e8, Vandoeuvre, France","institution_ids":["https://openalex.org/I4210110792","https://openalex.org/I1294671590"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5015675169","display_name":"Jamal Daafouz","orcid":"https://orcid.org/0000-0001-8313-8790"},"institutions":[{"id":"https://openalex.org/I4210110792","display_name":"Centre de Recherche en Automatique de Nancy","ror":"https://ror.org/022r5hc56","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I4210099203","https://openalex.org/I4210100260","https://openalex.org/I4210110792","https://openalex.org/I4210159245","https://openalex.org/I90183372"]},{"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"]},{"id":"https://openalex.org/I185839726","display_name":"Institut Universitaire de France","ror":"https://ror.org/055khg266","country_code":"FR","type":"education","lineage":["https://openalex.org/I185839726"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Jamal Daafouz","raw_affiliation_strings":["CRAN UMR 7039 CNRS, ENSEM, Nancy Universit\u00e8, Vandoeuvre, France","Institut Universitaire de France, France"],"affiliations":[{"raw_affiliation_string":"CRAN UMR 7039 CNRS, ENSEM, Nancy Universit\u00e8, Vandoeuvre, France","institution_ids":["https://openalex.org/I4210110792","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"Institut Universitaire de France, France","institution_ids":["https://openalex.org/I185839726"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5022375865","display_name":"Eug\u00eanio B. Castelan","orcid":"https://orcid.org/0000-0002-8079-3738"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Eugenio B. Castelan","raw_affiliation_strings":["DAS-CTC, UFSC, Florianopolis, Santa Catarina, Brazil"],"affiliations":[{"raw_affiliation_string":"DAS-CTC, UFSC, Florianopolis, Santa Catarina, Brazil","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5021012069"],"corresponding_institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I4210110792"],"apc_list":null,"apc_paid":null,"fwci":1.28677762,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.84898965,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"411","last_page":"416"},"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":0.995199978351593,"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":0.9937999844551086,"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":0.8120432496070862},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6961576342582703},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.5895765423774719},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5524807572364807},{"id":"https://openalex.org/keywords/lyapunov-redesign","display_name":"Lyapunov redesign","score":0.5512555241584778},{"id":"https://openalex.org/keywords/lyapunov-equation","display_name":"Lyapunov equation","score":0.5323225855827332},{"id":"https://openalex.org/keywords/lyapunov-exponent","display_name":"Lyapunov exponent","score":0.5148422122001648},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.504632830619812},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.4934288561344147},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4819793105125427},{"id":"https://openalex.org/keywords/control-lyapunov-function","display_name":"Control-Lyapunov function","score":0.4528225362300873},{"id":"https://openalex.org/keywords/lyapunov-optimization","display_name":"Lyapunov optimization","score":0.4373287558555603},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4357622265815735},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.36068013310432434},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.20208343863487244},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.17921233177185059},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.08076998591423035}],"concepts":[{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.8120432496070862},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6961576342582703},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5895765423774719},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5524807572364807},{"id":"https://openalex.org/C37935115","wikidata":"https://www.wikidata.org/wiki/Q6707085","display_name":"Lyapunov redesign","level":4,"score":0.5512555241584778},{"id":"https://openalex.org/C25854792","wikidata":"https://www.wikidata.org/wiki/Q1028945","display_name":"Lyapunov equation","level":4,"score":0.5323225855827332},{"id":"https://openalex.org/C191544260","wikidata":"https://www.wikidata.org/wiki/Q1238630","display_name":"Lyapunov exponent","level":3,"score":0.5148422122001648},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.504632830619812},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.4934288561344147},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4819793105125427},{"id":"https://openalex.org/C201030206","wikidata":"https://www.wikidata.org/wiki/Q5165805","display_name":"Control-Lyapunov function","level":5,"score":0.4528225362300873},{"id":"https://openalex.org/C101403955","wikidata":"https://www.wikidata.org/wiki/Q6707083","display_name":"Lyapunov optimization","level":5,"score":0.4373287558555603},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4357622265815735},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.36068013310432434},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.20208343863487244},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.17921233177185059},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.08076998591423035},{"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},{"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","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":1,"locations":[{"id":"doi:10.1109/cdc.2011.6161130","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2011.6161130","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W86892992","https://openalex.org/W1552094772","https://openalex.org/W1968114261","https://openalex.org/W1976148074","https://openalex.org/W1996952488","https://openalex.org/W2017940397","https://openalex.org/W2030373993","https://openalex.org/W2046874050","https://openalex.org/W2059366527","https://openalex.org/W2074840391","https://openalex.org/W2135575065","https://openalex.org/W2138387595","https://openalex.org/W2140999277","https://openalex.org/W2147908704","https://openalex.org/W3210839039","https://openalex.org/W4237663464","https://openalex.org/W6662170229"],"related_works":["https://openalex.org/W3217133416","https://openalex.org/W2383986032","https://openalex.org/W2349796700","https://openalex.org/W2534107666","https://openalex.org/W2496188264","https://openalex.org/W3194517843","https://openalex.org/W1970635650","https://openalex.org/W1983507234","https://openalex.org/W2126112326","https://openalex.org/W1979419366"],"abstract_inverted_index":{"This":[0,27],"paper":[1],"presents":[2],"a":[3,12,18,22,38,82],"new":[4,141],"class":[5],"of":[6,48,81,105,108,114,120,123,139,145],"Lur'e":[7],"type":[8],"Lyapunov":[9,39,128,142],"functions":[10],"for":[11,53,64,72],"discrete-time":[13],"switched":[14,19,83],"system":[15],"interconnected":[16],"with":[17,75],"nonlinearity":[20],"satisfying":[21],"mode-dependent":[23,31],"cone":[24],"bounded":[25],"condition.":[26],"function":[28,40,143],"includes":[29],"the":[30,54,65,88,103,106,121,124,127,137,140,146],"nonlinearity,":[32],"but":[33],"not":[34],"its":[35],"integral.":[36],"Such":[37],"allows":[41],"to":[42,101,135],"obtain":[43],"sufficient":[44,97],"conditions":[45,98],"in":[46,57,126],"terms":[47],"linear":[49,84],"matrix":[50],"inequalities":[51],"(LMI),":[52],"stability":[55,62,70],"analysis":[56,63,71],"two":[58],"different":[59],"frameworks:":[60],"global":[61],"considered":[66],"systems":[67,74],"and":[68,116,144],"local":[69],"these":[73,96],"an":[76,91],"additional":[77],"saturating":[78],"input":[79],"consisting":[80],"state":[85],"feedback.":[86],"In":[87],"second":[89],"case,":[90],"optimization":[92],"problem":[93],"based":[94],"on":[95],"is":[99],"provided":[100],"enlarge":[102],"estimation":[104],"basin":[107],"attraction,":[109],"which":[110],"may":[111],"be":[112],"composed":[113],"non-convex":[115],"disconnected":[117],"sets,":[118],"because":[119],"presence":[122],"nonlinearities":[125],"function.":[129],"Some":[130],"numerical":[131],"examples":[132],"are":[133],"presented":[134],"highlight":[136],"relevance":[138],"proposed":[147],"method.":[148]},"counts_by_year":[{"year":2015,"cited_by_count":2},{"year":2013,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
