{"id":"https://openalex.org/W2136683344","doi":"https://doi.org/10.1109/acc.2008.4587023","title":"Local stability analysis for uncertain nonlinear systems using a branch-and-bound algorithm","display_name":"Local stability analysis for uncertain nonlinear systems using a branch-and-bound algorithm","publication_year":2008,"publication_date":"2008-06-01","ids":{"openalex":"https://openalex.org/W2136683344","doi":"https://doi.org/10.1109/acc.2008.4587023","mag":"2136683344"},"language":"en","primary_location":{"id":"doi:10.1109/acc.2008.4587023","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2008.4587023","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2008 American Control Conference","raw_type":"proceedings-article"},"type":"conference-paper","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":"Ufuk Topcu","raw_affiliation_strings":["Department of Mechanical Engineering, University of California, Berkeley, CA, USA","Dept. of Mech. Eng., California Univ., Berkeley, CA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, University of California, Berkeley, CA, USA","institution_ids":["https://openalex.org/I95457486"]},{"raw_affiliation_string":"Dept. of Mech. Eng., California Univ., Berkeley, CA","institution_ids":["https://openalex.org/I95457486"]}]},{"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":"Andrew Packard","raw_affiliation_strings":["Department of Mechanical Engineering, University of California, Berkeley, CA, USA","Dept. of Mech. Eng., California Univ., Berkeley, CA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, University of California, Berkeley, CA, USA","institution_ids":["https://openalex.org/I95457486"]},{"raw_affiliation_string":"Dept. of Mech. Eng., California Univ., Berkeley, CA","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/I82514191","display_name":"Honeywell (United States)","ror":"https://ror.org/02t71h845","country_code":"US","type":"company","lineage":["https://openalex.org/I82514191"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Peter Seiler","raw_affiliation_strings":["Honeywell Laboratories in Minneapolis, MI, USA","[Honeywell Labs in Minneapolis, 55403, USA]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Honeywell Laboratories in Minneapolis, MI, USA","institution_ids":["https://openalex.org/I82514191"]},{"raw_affiliation_string":"[Honeywell Labs in Minneapolis, 55403, USA]","institution_ids":["https://openalex.org/I82514191"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5109125256","display_name":"Gary 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":"Gary Balas","raw_affiliation_strings":["Department of Aerospace Engineering Mechanics, University of Minnesota, Minneapolis, MI, USA","[Department of Aerospace Engineering and Mechanics, The University of Minnesota, Minneapolis, 55455, USA]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Aerospace Engineering Mechanics, University of Minnesota, Minneapolis, MI, USA","institution_ids":["https://openalex.org/I130238516"]},{"raw_affiliation_string":"[Department of Aerospace Engineering and Mechanics, The University of Minnesota, Minneapolis, 55455, 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":null,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":"7","issue":null,"first_page":"3428","last_page":"3433"},"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":0.9879000186920166,"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":0.9879000186920166,"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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9868999719619751,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10791","display_name":"Advanced Control Systems Optimization","score":0.9857000112533569,"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/parametric-statistics","display_name":"Parametric statistics","score":0.7018449902534485},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6811721324920654},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.6154319047927856},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6129578351974487},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.5631813406944275},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5568310022354126},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5284172296524048},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.49566972255706787},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4779896140098572},{"id":"https://openalex.org/keywords/lti-system-theory","display_name":"LTI system theory","score":0.4722784459590912},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.4701649844646454},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.44210296869277954},{"id":"https://openalex.org/keywords/robust-control","display_name":"Robust control","score":0.43716001510620117},{"id":"https://openalex.org/keywords/stability-theory","display_name":"Stability theory","score":0.4278532862663269},{"id":"https://openalex.org/keywords/nonlinear-dynamical-systems","display_name":"Nonlinear dynamical systems","score":0.41592341661453247},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3708382248878479},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.348526269197464},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3062542676925659},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2930137515068054},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.2430906891822815},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.14106184244155884},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11877474188804626},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.08808469772338867}],"concepts":[{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.7018449902534485},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6811721324920654},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.6154319047927856},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6129578351974487},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.5631813406944275},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5568310022354126},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5284172296524048},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.49566972255706787},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4779896140098572},{"id":"https://openalex.org/C87698059","wikidata":"https://www.wikidata.org/wiki/Q1808960","display_name":"LTI system theory","level":3,"score":0.4722784459590912},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.4701649844646454},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.44210296869277954},{"id":"https://openalex.org/C31531917","wikidata":"https://www.wikidata.org/wiki/Q915157","display_name":"Robust control","level":3,"score":0.43716001510620117},{"id":"https://openalex.org/C41949839","wikidata":"https://www.wikidata.org/wiki/Q1756677","display_name":"Stability theory","level":3,"score":0.4278532862663269},{"id":"https://openalex.org/C2983030100","wikidata":"https://www.wikidata.org/wiki/Q638328","display_name":"Nonlinear dynamical systems","level":3,"score":0.41592341661453247},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3708382248878479},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.348526269197464},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3062542676925659},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2930137515068054},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.2430906891822815},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.14106184244155884},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11877474188804626},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.08808469772338867},{"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/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","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":1,"locations":[{"id":"doi:10.1109/acc.2008.4587023","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2008.4587023","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2008 American Control Conference","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W814977041","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/W2116676017","https://openalex.org/W2122114813","https://openalex.org/W2130515279","https://openalex.org/W2141662368","https://openalex.org/W2151310265","https://openalex.org/W2179970775","https://openalex.org/W2570513205","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2056626217","https://openalex.org/W1541871911","https://openalex.org/W2050258033","https://openalex.org/W3185784018","https://openalex.org/W2184005427","https://openalex.org/W2118381768","https://openalex.org/W2148316232","https://openalex.org/W3212383242","https://openalex.org/W2079626172","https://openalex.org/W2981998189"],"abstract_inverted_index":{"We":[0,49],"propose":[1],"a":[2,54],"method":[3,52],"to":[4,30,45,75],"compute":[5],"invariant":[6,32],"subsets":[7,33],"of":[8,17,34],"the":[9,12,35,47,51,58,73,76],"region-of-attraction":[10],"for":[11],"asymptotically":[13],"stable":[14],"equilibrium":[15],"points":[16],"polynomial":[18],"dynamical":[19],"systems":[20],"with":[21,67],"bounded":[22],"parametric":[23],"uncertainty.":[24],"Parameter-independent":[25],"Lyapunov":[26],"functions":[27],"are":[28],"used":[29],"characterize":[31],"robust":[36],"region-of-attraction.":[37],"A":[38],"branch-and-bound":[39],"type":[40],"refinement":[41],"procedure":[42],"is":[43],"implemented":[44],"reduce":[46],"conservatism.":[48],"demonstrate":[50],"on":[53],"two-state":[55],"example":[56],"from":[57],"literature":[59],"and":[60,68],"five-state":[61],"controlled":[62],"short":[63],"period":[64],"aircraft":[65],"dynamics":[66],"without":[69],"time":[70],"delay":[71],"in":[72],"input":[74],"plant.":[77]},"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}