{"id":"https://openalex.org/W2167019375","doi":"https://doi.org/10.1109/tac.2009.2033751","title":"Robust Region-of-Attraction Estimation","display_name":"Robust Region-of-Attraction Estimation","publication_year":2009,"publication_date":"2009-11-23","ids":{"openalex":"https://openalex.org/W2167019375","doi":"https://doi.org/10.1109/tac.2009.2033751","mag":"2167019375"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2009.2033751","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2009.2033751","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/I122411786","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055","country_code":"US","type":"education","lineage":["https://openalex.org/I122411786"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"U. Topcu","raw_affiliation_strings":["Control and Dynamical Systems, California Institute of Technology, Pasadena, CA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Control and Dynamical Systems, California Institute of Technology, Pasadena, CA, USA","institution_ids":["https://openalex.org/I122411786"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5076844884","display_name":"Andrew 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.K. 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"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5009028512","display_name":"Peter Seiler","orcid":"https://orcid.org/0000-0003-3423-1109"},"institutions":[{"id":"https://openalex.org/I130238516","display_name":"University of Minnesota","ror":"https://ror.org/017zqws13","country_code":"US","type":"education","lineage":["https://openalex.org/I130238516"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"P. Seiler","raw_affiliation_strings":["Department of AeroSpace Engineering and Mechanics, University of Minnesota, Minneapolis, MN, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of AeroSpace Engineering and Mechanics, University of Minnesota, Minneapolis, MN, USA","institution_ids":["https://openalex.org/I130238516"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5109289277","display_name":"G.J. Balas","orcid":null},"institutions":[{"id":"https://openalex.org/I130238516","display_name":"University of Minnesota","ror":"https://ror.org/017zqws13","country_code":"US","type":"education","lineage":["https://openalex.org/I130238516"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"G.J. Balas","raw_affiliation_strings":["Department of AeroSpace Engineering and Mechanics, University of Minnesota, Minneapolis, MN, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of AeroSpace Engineering and Mechanics, University of Minnesota, Minneapolis, MN, USA","institution_ids":["https://openalex.org/I130238516"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":8.4018,"has_fulltext":false,"cited_by_count":118,"citation_normalized_percentile":{"value":0.97366126,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":100},"biblio":{"volume":"55","issue":"1","first_page":"137","last_page":"142"},"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":0.9973999857902527,"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":0.9973999857902527,"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":0.9965999722480774,"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":0.9965000152587891,"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/attraction","display_name":"Attraction","score":0.763702929019928},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.6471728086471558},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6379297971725464},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6271920204162598},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.6250655651092529},{"id":"https://openalex.org/keywords/robust-control","display_name":"Robust control","score":0.5948374271392822},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.549579918384552},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4802534878253937},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.4664060175418854},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.45735445618629456},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.4492288827896118},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4287313222885132},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.39992445707321167},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2441028654575348},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2369370460510254},{"id":"https://openalex.org/keywords/control-system","display_name":"Control system","score":0.2142246961593628},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.18318402767181396},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.13791286945343018},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.10079717636108398},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.08054834604263306},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07853749394416809},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.07101991772651672}],"concepts":[{"id":"https://openalex.org/C2778364177","wikidata":"https://www.wikidata.org/wiki/Q2247133","display_name":"Attraction","level":2,"score":0.763702929019928},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.6471728086471558},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6379297971725464},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6271920204162598},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.6250655651092529},{"id":"https://openalex.org/C31531917","wikidata":"https://www.wikidata.org/wiki/Q915157","display_name":"Robust control","level":3,"score":0.5948374271392822},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.549579918384552},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4802534878253937},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.4664060175418854},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.45735445618629456},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.4492288827896118},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4287313222885132},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.39992445707321167},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2441028654575348},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2369370460510254},{"id":"https://openalex.org/C17500928","wikidata":"https://www.wikidata.org/wiki/Q959968","display_name":"Control system","level":2,"score":0.2142246961593628},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.18318402767181396},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.13791286945343018},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.10079717636108398},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.08054834604263306},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07853749394416809},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.07101991772651672},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tac.2009.2033751","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2009.2033751","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:authors.library.caltech.edu:17413","is_oa":false,"landing_page_url":"https://resolver.caltech.edu/CaltechAUTHORS:20100208-095827914","pdf_url":null,"source":{"id":"https://openalex.org/S4306402161","display_name":"CaltechAUTHORS (California Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I122411786","host_organization_name":"California Institute of Technology","host_organization_lineage":["https://openalex.org/I122411786"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G7090116110","display_name":null,"funder_award_id":"FA9550","funder_id":"https://openalex.org/F4320332467","funder_display_name":"U.S. Air Force"}],"funders":[{"id":"https://openalex.org/F4320332467","display_name":"U.S. Air Force","ror":"https://ror.org/006gmme17"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W11977949","https://openalex.org/W94566284","https://openalex.org/W184169746","https://openalex.org/W814977041","https://openalex.org/W1571355869","https://openalex.org/W1967184028","https://openalex.org/W1992402930","https://openalex.org/W2013840602","https://openalex.org/W2021313930","https://openalex.org/W2023285936","https://openalex.org/W2060602079","https://openalex.org/W2078899217","https://openalex.org/W2104957613","https://openalex.org/W2106985815","https://openalex.org/W2116586985","https://openalex.org/W2116676017","https://openalex.org/W2122114813","https://openalex.org/W2130515279","https://openalex.org/W2141662368","https://openalex.org/W2144931885","https://openalex.org/W2161936466","https://openalex.org/W2170988755","https://openalex.org/W2179970775","https://openalex.org/W2400094359","https://openalex.org/W4285719527","https://openalex.org/W6683582569","https://openalex.org/W6685016740"],"related_works":["https://openalex.org/W1550017747","https://openalex.org/W2101888154","https://openalex.org/W36592976","https://openalex.org/W2743916083","https://openalex.org/W2378979564","https://openalex.org/W2067224748","https://openalex.org/W1981979037","https://openalex.org/W1505013685","https://openalex.org/W2045297213","https://openalex.org/W1510650626"],"abstract_inverted_index":{"We":[0,45],"propose":[1],"a":[2],"method":[3,48],"to":[4,29],"compute":[5],"invariant":[6,31],"subsets":[7,32],"of":[8,16,33],"the":[9,34,43,47,53],"region-of-attraction":[10],"for":[11],"asymptotically":[12],"stable":[13],"equilibrium":[14],"points":[15],"polynomial":[17],"dynamical":[18],"systems":[19],"with":[20],"bounded":[21],"parametric":[22],"uncertainty.":[23],"Parameter-independent":[24],"Lyapunov":[25],"functions":[26],"are":[27],"used":[28],"characterize":[30],"robust":[35],"region-of-attraction.":[36],"A":[37],"branch-and-bound":[38],"type":[39],"refinement":[40],"procedure":[41],"reduces":[42],"conservatism.":[44],"demonstrate":[46],"on":[49],"an":[50],"example":[51],"from":[52],"literature":[54],"and":[55],"uncertain":[56],"controlled":[57],"short-period":[58],"aircraft":[59],"dynamics.":[60]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":11},{"year":2019,"cited_by_count":15},{"year":2018,"cited_by_count":11},{"year":2017,"cited_by_count":9},{"year":2016,"cited_by_count":11},{"year":2015,"cited_by_count":8},{"year":2014,"cited_by_count":6},{"year":2013,"cited_by_count":9},{"year":2012,"cited_by_count":6}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}