{"id":"https://openalex.org/W2003652915","doi":"https://doi.org/10.1109/cdc.2011.6161493","title":"Converse results on existence of sum of squares Lyapunov functions","display_name":"Converse results on existence of sum of squares Lyapunov functions","publication_year":2011,"publication_date":"2011-12-01","ids":{"openalex":"https://openalex.org/W2003652915","doi":"https://doi.org/10.1109/cdc.2011.6161493","mag":"2003652915"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2011.6161493","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2011.6161493","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":true,"oa_status":"green","oa_url":"http://hdl.handle.net/1721.1/72483","any_repository_has_fulltext":true},"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/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Amir Ali Ahmadi","raw_affiliation_strings":["Laboratory for Information and Decision Systems, Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, USA","[Laboratory for Information and Decision Systems, Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, USA]"],"affiliations":[{"raw_affiliation_string":"Laboratory for Information and Decision Systems, Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, USA","institution_ids":["https://openalex.org/I63966007"]},{"raw_affiliation_string":"[Laboratory for Information and Decision Systems, Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, USA]","institution_ids":["https://openalex.org/I63966007"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5031935416","display_name":"Pablo A. Parrilo","orcid":"https://orcid.org/0000-0003-1132-8477"},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Pablo A. Parrilo","raw_affiliation_strings":["Laboratory for Information and Decision Systems, Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, USA","[Laboratory for Information and Decision Systems, Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, USA]"],"affiliations":[{"raw_affiliation_string":"Laboratory for Information and Decision Systems, Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, USA","institution_ids":["https://openalex.org/I63966007"]},{"raw_affiliation_string":"[Laboratory for Information and Decision Systems, Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, USA]","institution_ids":["https://openalex.org/I63966007"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5101485690"],"corresponding_institution_ids":["https://openalex.org/I63966007"],"apc_list":null,"apc_paid":null,"fwci":7.88,"has_fulltext":false,"cited_by_count":35,"citation_normalized_percentile":{"value":0.97020957,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"6516","last_page":"6521"},"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":0.9991000294685364,"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":0.9991000294685364,"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":0.9984999895095825,"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":0.9973000288009644,"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":0.8298416137695312},{"id":"https://openalex.org/keywords/lyapunov-exponent","display_name":"Lyapunov exponent","score":0.789347767829895},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7675997018814087},{"id":"https://openalex.org/keywords/lyapunov-equation","display_name":"Lyapunov equation","score":0.6785358190536499},{"id":"https://openalex.org/keywords/lyapunov-redesign","display_name":"Lyapunov redesign","score":0.6448462605476379},{"id":"https://openalex.org/keywords/homogeneous-polynomial","display_name":"Homogeneous polynomial","score":0.6359928846359253},{"id":"https://openalex.org/keywords/lyapunov-optimization","display_name":"Lyapunov optimization","score":0.6278083920478821},{"id":"https://openalex.org/keywords/counterexample","display_name":"Counterexample","score":0.623869776725769},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5723456144332886},{"id":"https://openalex.org/keywords/explained-sum-of-squares","display_name":"Explained sum of squares","score":0.5387654304504395},{"id":"https://openalex.org/keywords/converse","display_name":"Converse","score":0.5138073563575745},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4604744017124176},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.42132487893104553},{"id":"https://openalex.org/keywords/control-lyapunov-function","display_name":"Control-Lyapunov function","score":0.4194566011428833},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.2831278443336487},{"id":"https://openalex.org/keywords/matrix-polynomial","display_name":"Matrix polynomial","score":0.2656900882720947},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2368568480014801},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.2017834186553955}],"concepts":[{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.8298416137695312},{"id":"https://openalex.org/C191544260","wikidata":"https://www.wikidata.org/wiki/Q1238630","display_name":"Lyapunov exponent","level":3,"score":0.789347767829895},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7675997018814087},{"id":"https://openalex.org/C25854792","wikidata":"https://www.wikidata.org/wiki/Q1028945","display_name":"Lyapunov equation","level":4,"score":0.6785358190536499},{"id":"https://openalex.org/C37935115","wikidata":"https://www.wikidata.org/wiki/Q6707085","display_name":"Lyapunov redesign","level":4,"score":0.6448462605476379},{"id":"https://openalex.org/C17103678","wikidata":"https://www.wikidata.org/wiki/Q1474074","display_name":"Homogeneous polynomial","level":4,"score":0.6359928846359253},{"id":"https://openalex.org/C101403955","wikidata":"https://www.wikidata.org/wiki/Q6707083","display_name":"Lyapunov optimization","level":5,"score":0.6278083920478821},{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.623869776725769},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5723456144332886},{"id":"https://openalex.org/C49847556","wikidata":"https://www.wikidata.org/wiki/Q3964631","display_name":"Explained sum of squares","level":2,"score":0.5387654304504395},{"id":"https://openalex.org/C2776809875","wikidata":"https://www.wikidata.org/wiki/Q1375963","display_name":"Converse","level":2,"score":0.5138073563575745},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4604744017124176},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.42132487893104553},{"id":"https://openalex.org/C201030206","wikidata":"https://www.wikidata.org/wiki/Q5165805","display_name":"Control-Lyapunov function","level":5,"score":0.4194566011428833},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2831278443336487},{"id":"https://openalex.org/C101044782","wikidata":"https://www.wikidata.org/wiki/Q6787887","display_name":"Matrix polynomial","level":3,"score":0.2656900882720947},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2368568480014801},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.2017834186553955},{"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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/cdc.2011.6161493","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2011.6161493","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:dspace.mit.edu:1721.1/72483","is_oa":true,"landing_page_url":"http://hdl.handle.net/1721.1/72483","pdf_url":null,"source":{"id":"https://openalex.org/S4306400425","display_name":"DSpace@MIT (Massachusetts Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I63966007","host_organization_name":"Massachusetts Institute of Technology","host_organization_lineage":["https://openalex.org/I63966007"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"MIT web domain","raw_type":"http://purl.org/eprint/type/ConferencePaper"},{"id":"pmh:oai:zenodo.org:1265804","is_oa":true,"landing_page_url":"https://zenodo.org/record/1265804","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:dspace.mit.edu:1721.1/72483","is_oa":true,"landing_page_url":"http://hdl.handle.net/1721.1/72483","pdf_url":null,"source":{"id":"https://openalex.org/S4306400425","display_name":"DSpace@MIT (Massachusetts Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I63966007","host_organization_name":"Massachusetts Institute of Technology","host_organization_lineage":["https://openalex.org/I63966007"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"MIT web domain","raw_type":"http://purl.org/eprint/type/ConferencePaper"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W68192900","https://openalex.org/W431400460","https://openalex.org/W1481077264","https://openalex.org/W1530960252","https://openalex.org/W1591868040","https://openalex.org/W1600295805","https://openalex.org/W1967184028","https://openalex.org/W1971837993","https://openalex.org/W1997370679","https://openalex.org/W2006116648","https://openalex.org/W2015144913","https://openalex.org/W2026018724","https://openalex.org/W2065053468","https://openalex.org/W2079135578","https://openalex.org/W2080688746","https://openalex.org/W2087208242","https://openalex.org/W2098511113","https://openalex.org/W2099212405","https://openalex.org/W2101676748","https://openalex.org/W2103952421","https://openalex.org/W2104730516","https://openalex.org/W2107104458","https://openalex.org/W2121680057","https://openalex.org/W2133404041","https://openalex.org/W2133913867","https://openalex.org/W2145328298","https://openalex.org/W2155689575","https://openalex.org/W2161507975","https://openalex.org/W2170665905","https://openalex.org/W2313809083","https://openalex.org/W2912522929","https://openalex.org/W2950795273","https://openalex.org/W3105811395","https://openalex.org/W6666863230"],"related_works":["https://openalex.org/W3217133416","https://openalex.org/W2383986032","https://openalex.org/W2349796700","https://openalex.org/W1970635650","https://openalex.org/W2496188264","https://openalex.org/W2546013078","https://openalex.org/W1488834356","https://openalex.org/W2524522145","https://openalex.org/W1996715315","https://openalex.org/W2003652915"],"abstract_inverted_index":{"Despite":[0],"the":[1,15,44,47,69,73,106],"pervasiveness":[2],"of":[3,5,12,18,46,83,96,108,129],"sum":[4],"squares":[6],"(sos)":[7],"techniques":[8],"in":[9],"Lyapunov":[10,21,26,49,62,86,99,124],"analysis":[11],"dynamical":[13],"systems,":[14],"converse":[16,122],"question":[17],"whether":[19],"sos":[20,54,103,123],"functions":[22,27],"exist":[23,28],"whenever":[24],"polynomial":[25,48,85,91,98],"has":[29],"remained":[30],"elusive.":[31],"In":[32],"this":[33],"paper,":[34],"we":[35,79],"first":[36],"show":[37],"via":[38],"an":[39],"explicit":[40],"counterexample":[41],"that":[42,81,101,105],"if":[43,72],"degree":[45,74],"function":[50,63,87,100],"is":[51,75,102,111,117],"fixed,":[52],"then":[53],"programming":[55],"can":[56],"fail":[57],"to":[58,77,119],"find":[59],"a":[60,84,89,97,121],"valid":[61],"even":[64],"though":[65],"one":[66],"exists.":[67],"On":[68],"other":[70],"hand,":[71],"allowed":[76],"increase,":[78],"prove":[80],"existence":[82,95],"for":[88,126],"homogeneous":[90],"vector":[92],"field":[93],"implies":[94],"and":[104],"negative":[107],"its":[109],"derivative":[110],"also":[112],"sos.":[113],"The":[114],"latter":[115],"result":[116],"extended":[118],"develop":[120],"theorem":[125],"robust":[127],"stability":[128],"switched":[130],"linear":[131],"systems.":[132]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":3},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":3}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2016-06-24T00:00:00"}
