{"id":"https://openalex.org/W2080611878","doi":"https://doi.org/10.1109/cdc.2013.6759968","title":"Switched stability of nonlinear systems via SOS-convex Lyapunov functions and semidefinite programming","display_name":"Switched stability of nonlinear systems via SOS-convex Lyapunov functions and semidefinite programming","publication_year":2013,"publication_date":"2013-12-01","ids":{"openalex":"https://openalex.org/W2080611878","doi":"https://doi.org/10.1109/cdc.2013.6759968","mag":"2080611878"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2013.6759968","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2013.6759968","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"52nd IEEE Conference on Decision and Control","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/A5101485690","display_name":"Amir Ali Ahmadi","orcid":"https://orcid.org/0009-0001-5743-354X"},"institutions":[{"id":"https://openalex.org/I1341412227","display_name":"IBM (United States)","ror":"https://ror.org/05hh8d621","country_code":"US","type":"company","lineage":["https://openalex.org/I1341412227"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Amir Ali Ahmadi","raw_affiliation_strings":["Department of Business Analytics and Mathematical Sciences, IBM Watson Research Center","Dept. of Bus. Analytics & Math. Sci., IBM Watson Res. Center, Yorktown Heights, NY, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Business Analytics and Mathematical Sciences, IBM Watson Research Center","institution_ids":["https://openalex.org/I1341412227"]},{"raw_affiliation_string":"Dept. of Bus. Analytics & Math. Sci., IBM Watson Res. Center, Yorktown Heights, NY, USA","institution_ids":["https://openalex.org/I1341412227"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5056625594","display_name":"Rapha\u00ebl M. Jungers","orcid":"https://orcid.org/0000-0002-7789-0940"},"institutions":[{"id":"https://openalex.org/I95674353","display_name":"UCLouvain","ror":"https://ror.org/02495e989","country_code":"BE","type":"education","lineage":["https://openalex.org/I95674353"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Raphael M. Jungers","raw_affiliation_strings":["ICTEAM Institute, Universit\u00e9 catholique de Louvain","ICTEAM Inst., Univ. Catholique de Louvain, Louvain la Neuve, Belgium"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ICTEAM Institute, Universit\u00e9 catholique de Louvain","institution_ids":["https://openalex.org/I95674353"]},{"raw_affiliation_string":"ICTEAM Inst., Univ. Catholique de Louvain, Louvain la Neuve, Belgium","institution_ids":["https://openalex.org/I95674353"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.5451,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.90281333,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"727","last_page":"732"},"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":0.9988999962806702,"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":0.9988999962806702,"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/T10621","display_name":"Gene Regulatory Network Analysis","score":0.9972000122070312,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T10791","display_name":"Advanced Control Systems Optimization","score":0.9926000237464905,"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":0.7607976794242859},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7198881506919861},{"id":"https://openalex.org/keywords/lyapunov-redesign","display_name":"Lyapunov redesign","score":0.6432784795761108},{"id":"https://openalex.org/keywords/semidefinite-programming","display_name":"Semidefinite programming","score":0.619853138923645},{"id":"https://openalex.org/keywords/lyapunov-equation","display_name":"Lyapunov equation","score":0.5969735980033875},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5295425653457642},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.5142545104026794},{"id":"https://openalex.org/keywords/lyapunov-exponent","display_name":"Lyapunov exponent","score":0.4929814338684082},{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.4569436013698578},{"id":"https://openalex.org/keywords/linear-matrix-inequality","display_name":"Linear matrix inequality","score":0.4400777220726013},{"id":"https://openalex.org/keywords/linearization","display_name":"Linearization","score":0.43191292881965637},{"id":"https://openalex.org/keywords/control-lyapunov-function","display_name":"Control-Lyapunov function","score":0.42657002806663513},{"id":"https://openalex.org/keywords/convex-analysis","display_name":"Convex analysis","score":0.41814321279525757},{"id":"https://openalex.org/keywords/convex-combination","display_name":"Convex combination","score":0.41257038712501526},{"id":"https://openalex.org/keywords/convex-hull","display_name":"Convex hull","score":0.4103701710700989},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4026281237602234},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.33299529552459717},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.2710345983505249},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.252662718296051},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.16800862550735474},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.14335262775421143}],"concepts":[{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.7607976794242859},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7198881506919861},{"id":"https://openalex.org/C37935115","wikidata":"https://www.wikidata.org/wiki/Q6707085","display_name":"Lyapunov redesign","level":4,"score":0.6432784795761108},{"id":"https://openalex.org/C101901036","wikidata":"https://www.wikidata.org/wiki/Q2269096","display_name":"Semidefinite programming","level":2,"score":0.619853138923645},{"id":"https://openalex.org/C25854792","wikidata":"https://www.wikidata.org/wiki/Q1028945","display_name":"Lyapunov equation","level":4,"score":0.5969735980033875},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5295425653457642},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.5142545104026794},{"id":"https://openalex.org/C191544260","wikidata":"https://www.wikidata.org/wiki/Q1238630","display_name":"Lyapunov exponent","level":3,"score":0.4929814338684082},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.4569436013698578},{"id":"https://openalex.org/C201829737","wikidata":"https://www.wikidata.org/wiki/Q2022760","display_name":"Linear matrix inequality","level":2,"score":0.4400777220726013},{"id":"https://openalex.org/C11210021","wikidata":"https://www.wikidata.org/wiki/Q1520713","display_name":"Linearization","level":3,"score":0.43191292881965637},{"id":"https://openalex.org/C201030206","wikidata":"https://www.wikidata.org/wiki/Q5165805","display_name":"Control-Lyapunov function","level":5,"score":0.42657002806663513},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.41814321279525757},{"id":"https://openalex.org/C111110010","wikidata":"https://www.wikidata.org/wiki/Q2627315","display_name":"Convex combination","level":4,"score":0.41257038712501526},{"id":"https://openalex.org/C206194317","wikidata":"https://www.wikidata.org/wiki/Q1138624","display_name":"Convex hull","level":3,"score":0.4103701710700989},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4026281237602234},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.33299529552459717},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2710345983505249},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.252662718296051},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.16800862550735474},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14335262775421143},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cdc.2013.6759968","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2013.6759968","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"52nd IEEE Conference on Decision and Control","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W653291882","https://openalex.org/W1480919729","https://openalex.org/W1481077264","https://openalex.org/W1542648917","https://openalex.org/W1549626567","https://openalex.org/W1569239057","https://openalex.org/W1597116596","https://openalex.org/W1884347414","https://openalex.org/W1967184028","https://openalex.org/W1974962384","https://openalex.org/W1978242229","https://openalex.org/W1981518949","https://openalex.org/W1992253023","https://openalex.org/W1997370679","https://openalex.org/W2003950764","https://openalex.org/W2015144913","https://openalex.org/W2018403127","https://openalex.org/W2020979852","https://openalex.org/W2035453684","https://openalex.org/W2036117572","https://openalex.org/W2040235632","https://openalex.org/W2080688746","https://openalex.org/W2082419392","https://openalex.org/W2084970142","https://openalex.org/W2103764200","https://openalex.org/W2118863844","https://openalex.org/W2129997623","https://openalex.org/W2133404041","https://openalex.org/W2136991030","https://openalex.org/W2138601039","https://openalex.org/W2145328298","https://openalex.org/W2155689575","https://openalex.org/W2255400221","https://openalex.org/W2911681356","https://openalex.org/W3103158853","https://openalex.org/W3105811395","https://openalex.org/W4238257903","https://openalex.org/W4256127285"],"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/W2333471870","https://openalex.org/W2091455539","https://openalex.org/W2374426356"],"abstract_inverted_index":{"We":[0,36],"introduce":[1],"the":[2,57,67,90,97,103,140,143,157,173,193],"concept":[3],"of":[4,11,26,52,70,106,110,115,131,142,146,168,183,195],"sos-convex":[5,72,147],"Lyapunov":[6,19,41,73,83,119,135,148],"functions":[7,20,42,149],"for":[8,49,126,172],"stability":[9,50,171],"analysis":[10,51],"discrete":[12],"time":[13],"switched":[14,53,98,127,158,170],"systems.":[15,55],"These":[16],"are":[17,43],"polynomial":[18,40,82,182],"that":[21,38,66,95],"have":[22],"an":[23,63,71,190],"algebraic":[24],"certificate":[25],"convexity,":[27],"and":[28,47],"can":[29,75,151,188],"be":[30,76,152],"efficiently":[31],"found":[32],"by":[33],"semidefinite":[34],"programming.":[35],"show":[37,61,94],"convex":[39,104,133],"universal":[44],"(i.e.,":[45],"necessary":[46],"sufficient)":[48],"linear":[54],"On":[56],"other":[58],"hand,":[59],"we":[60,93],"via":[62],"explicit":[64],"example":[65,177],"minimum":[68],"degree":[69,184],"function":[74,120,136],"arbitrarily":[77],"higher":[78],"than":[79,186],"a":[80,107,116,123,132],"(non-convex)":[81],"function.":[84],"(The":[85],"proof":[86,167],"is":[87,100,121,178],"omitted.)":[88],"In":[89],"second":[91],"part,":[92],"if":[96],"system":[99],"defined":[101],"as":[102],"hull":[105],"finite":[108],"number":[109],"nonlinear":[111,159,174],"functions,":[112],"then":[113],"existence":[114,130],"non-convex":[117],"common":[118,134],"not":[122],"sufficient":[124],"condition":[125],"stability,":[128],"but":[129],"is.":[137],"This":[138],"shows":[139],"usefulness":[141],"computational":[144],"machinery":[145],"which":[150],"applied":[153],"either":[154],"directly":[155],"to":[156,162,165,192],"system,":[160],"or":[161],"its":[163],"linearization,":[164],"provide":[166,189],"local":[169],"system.":[175],"An":[176],"given":[179],"where":[180],"no":[181],"less":[185],"14":[187],"estimate":[191],"region":[194],"attraction":[196],"under":[197],"arbitrary":[198],"switching.":[199]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}