{"id":"https://openalex.org/W2161936466","doi":"https://doi.org/10.1109/tac.2009.2017157","title":"Local Stability Analysis for Uncertain Nonlinear Systems","display_name":"Local Stability Analysis for Uncertain Nonlinear Systems","publication_year":2009,"publication_date":"2009-05-01","ids":{"openalex":"https://openalex.org/W2161936466","doi":"https://doi.org/10.1109/tac.2009.2017157","mag":"2161936466"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2009.2017157","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2009.2017157","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-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/A5068441112","display_name":"Ufuk Topcu","orcid":"https://orcid.org/0000-0003-0819-9985"},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"U. Topcu","raw_affiliation_strings":["Department of Mechanical Engineering, University of California, Berkeley, CA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, University of California, Berkeley, CA, USA","institution_ids":["https://openalex.org/I95457486"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5045903370","display_name":"Andy Packard","orcid":null},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"A. Packard","raw_affiliation_strings":["Department of Mechanical Engineering, University of California, Berkeley, CA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, University of California, Berkeley, CA, USA","institution_ids":["https://openalex.org/I95457486"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I95457486"],"apc_list":null,"apc_paid":null,"fwci":5.8625,"has_fulltext":false,"cited_by_count":54,"citation_normalized_percentile":{"value":0.97603011,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"54","issue":"5","first_page":"1042","last_page":"1047"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10046","display_name":"Stability and Control of Uncertain 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"}},{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.998199999332428,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6638972759246826},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.654747724533081},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.6066982746124268},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.5749819278717041},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5706797242164612},{"id":"https://openalex.org/keywords/nonlinear-dynamical-systems","display_name":"Nonlinear dynamical systems","score":0.5481588244438171},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4819743037223816},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.45467787981033325},{"id":"https://openalex.org/keywords/vector-field","display_name":"Vector field","score":0.4105975031852722},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3721664547920227},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.3348659574985504},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.19414809346199036},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1841762661933899},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.18390414118766785},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.071534663438797},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.07036289572715759}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6638972759246826},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.654747724533081},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.6066982746124268},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.5749819278717041},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5706797242164612},{"id":"https://openalex.org/C2983030100","wikidata":"https://www.wikidata.org/wiki/Q638328","display_name":"Nonlinear dynamical systems","level":3,"score":0.5481588244438171},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4819743037223816},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.45467787981033325},{"id":"https://openalex.org/C91188154","wikidata":"https://www.wikidata.org/wiki/Q186247","display_name":"Vector field","level":2,"score":0.4105975031852722},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3721664547920227},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3348659574985504},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.19414809346199036},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1841762661933899},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.18390414118766785},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.071534663438797},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.07036289572715759},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","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/tac.2009.2017157","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2009.2017157","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.543.4438","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.543.4438","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://jagger.berkeley.edu/~pack/library/acc2008.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W94566284","https://openalex.org/W184169746","https://openalex.org/W814977041","https://openalex.org/W1503221585","https://openalex.org/W1542709735","https://openalex.org/W1544904396","https://openalex.org/W1568307856","https://openalex.org/W1967184028","https://openalex.org/W1967344706","https://openalex.org/W1967722865","https://openalex.org/W1992402930","https://openalex.org/W2013840602","https://openalex.org/W2021313930","https://openalex.org/W2023285936","https://openalex.org/W2043363105","https://openalex.org/W2060602079","https://openalex.org/W2078899217","https://openalex.org/W2104730516","https://openalex.org/W2104957613","https://openalex.org/W2106985815","https://openalex.org/W2116586985","https://openalex.org/W2116676017","https://openalex.org/W2141662368","https://openalex.org/W2150001254","https://openalex.org/W2151310265","https://openalex.org/W2153343992","https://openalex.org/W2170988755","https://openalex.org/W2179970775","https://openalex.org/W2312849699","https://openalex.org/W2400094359","https://openalex.org/W2491336180","https://openalex.org/W3151056277","https://openalex.org/W4285719527","https://openalex.org/W6682780176","https://openalex.org/W6685016740"],"related_works":["https://openalex.org/W1541871911","https://openalex.org/W2910118375","https://openalex.org/W2184005427","https://openalex.org/W3185784018","https://openalex.org/W3212383242","https://openalex.org/W2050258033","https://openalex.org/W2148316232","https://openalex.org/W2056626217","https://openalex.org/W2074935838","https://openalex.org/W2118381768"],"abstract_inverted_index":{"We":[0,23,77],"propose":[1],"a":[2,88],"method":[3,80],"to":[4],"compute":[5],"provably":[6],"invariant":[7,72],"subsets":[8,73],"of":[9,18,64,74],"the":[10,13,45,65,75,79,85],"region-of-attraction":[11],"for":[12],"asymptotically":[14],"stable":[15],"equilibrium":[16],"points":[17],"uncertain":[19,39],"nonlinear":[20],"dynamical":[21],"systems.":[22],"consider":[24],"polynomial":[25,33,42],"dynamics":[26,93],"with":[27],"perturbations":[28],"that":[29],"either":[30],"obey":[31],"local":[32],"bounds":[34],"or":[35],"are":[36],"described":[37],"by":[38,53],"parameters":[40],"multiplying":[41],"terms":[43],"in":[44,56],"vector":[46],"field.":[47],"This":[48],"uncertainty":[49],"description":[50],"is":[51],"motivated":[52],"both":[54],"incapabilities":[55],"modeling,":[57],"as":[58,60],"well":[59],"bilinearity":[61],"and":[62,87],"dimension":[63],"sum-of-squares":[66],"programming":[67],"problems":[68],"whose":[69],"solutions":[70],"provide":[71],"region-of-attraction.":[76],"demonstrate":[78],"on":[81],"three":[82],"examples":[83],"from":[84],"literature":[86],"controlled":[89],"short":[90],"period":[91],"aircraft":[92],"example.":[94]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":4},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":6}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}