{"id":"https://openalex.org/W2162379117","doi":"https://doi.org/10.1109/acc.2011.5991021","title":"Synergistic Lyapunov functions and backstepping hybrid feedbacks","display_name":"Synergistic Lyapunov functions and backstepping hybrid feedbacks","publication_year":2011,"publication_date":"2011-06-01","ids":{"openalex":"https://openalex.org/W2162379117","doi":"https://doi.org/10.1109/acc.2011.5991021","mag":"2162379117"},"language":"en","primary_location":{"id":"doi:10.1109/acc.2011.5991021","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2011.5991021","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2011 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/A5043506578","display_name":"Christopher G. Mayhew","orcid":null},"institutions":[{"id":"https://openalex.org/I4210120115","display_name":"Robert Bosch (United States)","ror":"https://ror.org/02venad53","country_code":"US","type":"company","lineage":["https://openalex.org/I4210120115","https://openalex.org/I889804353"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Christopher G. Mayhew","raw_affiliation_strings":["Robert Bosch Limited Liability Company, Palo Alto, CA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Robert Bosch Limited Liability Company, Palo Alto, CA, USA","institution_ids":["https://openalex.org/I4210120115"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028224738","display_name":"Ricardo G. Sanfelice","orcid":"https://orcid.org/0000-0002-6671-5362"},"institutions":[{"id":"https://openalex.org/I138006243","display_name":"University of Arizona","ror":"https://ror.org/03m2x1q45","country_code":"US","type":"education","lineage":["https://openalex.org/I138006243"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ricardo G. Sanfelice","raw_affiliation_strings":["Department of AeroSpace and Mechanical Engineering, University of Arizona Tucson, Tucson, AZ, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of AeroSpace and Mechanical Engineering, University of Arizona Tucson, Tucson, AZ, USA","institution_ids":["https://openalex.org/I138006243"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5002737786","display_name":"Andrew R. Teel","orcid":"https://orcid.org/0000-0002-6508-0879"},"institutions":[{"id":"https://openalex.org/I154570441","display_name":"University of California, Santa Barbara","ror":"https://ror.org/02t274463","country_code":"US","type":"education","lineage":["https://openalex.org/I154570441"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Andrew R. Teel","raw_affiliation_strings":["Center for Control Engineering and Computation, Electrical and Computer Engineering Department, University of California, Santa Barbara, CA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Control Engineering and Computation, Electrical and Computer Engineering Department, University of California, Santa Barbara, CA, USA","institution_ids":["https://openalex.org/I154570441"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.4937,"has_fulltext":false,"cited_by_count":26,"citation_normalized_percentile":{"value":0.93244896,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"3203","last_page":"3208"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.9998000264167786,"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/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.9998000264167786,"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/T10040","display_name":"Adaptive Control of Nonlinear Systems","score":0.9995999932289124,"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/T11394","display_name":"Dynamics and Control of Mechanical Systems","score":0.9976000189781189,"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/backstepping","display_name":"Backstepping","score":0.8933005332946777},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.7247800827026367},{"id":"https://openalex.org/keywords/parametrization","display_name":"Parametrization (atmospheric modeling)","score":0.6792830228805542},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.5997500419616699},{"id":"https://openalex.org/keywords/lyapunov-redesign","display_name":"Lyapunov redesign","score":0.5620898604393005},{"id":"https://openalex.org/keywords/quaternion","display_name":"Quaternion","score":0.5171146392822266},{"id":"https://openalex.org/keywords/controller","display_name":"Controller (irrigation)","score":0.48579978942871094},{"id":"https://openalex.org/keywords/integrator","display_name":"Integrator","score":0.4777188301086426},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4547833502292633},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.4341081976890564},{"id":"https://openalex.org/keywords/control-lyapunov-function","display_name":"Control-Lyapunov function","score":0.42021942138671875},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.36089062690734863},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.34616541862487793},{"id":"https://openalex.org/keywords/adaptive-control","display_name":"Adaptive control","score":0.2616521418094635},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2058727741241455},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.20211046934127808},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.14724236726760864},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.0900481641292572},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07389360666275024},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.07322186231613159}],"concepts":[{"id":"https://openalex.org/C72218879","wikidata":"https://www.wikidata.org/wiki/Q4839759","display_name":"Backstepping","level":4,"score":0.8933005332946777},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.7247800827026367},{"id":"https://openalex.org/C202887219","wikidata":"https://www.wikidata.org/wiki/Q3895221","display_name":"Parametrization (atmospheric modeling)","level":3,"score":0.6792830228805542},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5997500419616699},{"id":"https://openalex.org/C37935115","wikidata":"https://www.wikidata.org/wiki/Q6707085","display_name":"Lyapunov redesign","level":4,"score":0.5620898604393005},{"id":"https://openalex.org/C200127275","wikidata":"https://www.wikidata.org/wiki/Q173853","display_name":"Quaternion","level":2,"score":0.5171146392822266},{"id":"https://openalex.org/C203479927","wikidata":"https://www.wikidata.org/wiki/Q5165939","display_name":"Controller (irrigation)","level":2,"score":0.48579978942871094},{"id":"https://openalex.org/C79518650","wikidata":"https://www.wikidata.org/wiki/Q2081431","display_name":"Integrator","level":3,"score":0.4777188301086426},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4547833502292633},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4341081976890564},{"id":"https://openalex.org/C201030206","wikidata":"https://www.wikidata.org/wiki/Q5165805","display_name":"Control-Lyapunov function","level":5,"score":0.42021942138671875},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.36089062690734863},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.34616541862487793},{"id":"https://openalex.org/C107464732","wikidata":"https://www.wikidata.org/wiki/Q235781","display_name":"Adaptive control","level":3,"score":0.2616521418094635},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2058727741241455},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.20211046934127808},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.14724236726760864},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.0900481641292572},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07389360666275024},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.07322186231613159},{"id":"https://openalex.org/C2776257435","wikidata":"https://www.wikidata.org/wiki/Q1576430","display_name":"Bandwidth (computing)","level":2,"score":0.0},{"id":"https://openalex.org/C74902906","wikidata":"https://www.wikidata.org/wiki/Q1190858","display_name":"Radiative transfer","level":2,"score":0.0},{"id":"https://openalex.org/C6557445","wikidata":"https://www.wikidata.org/wiki/Q173113","display_name":"Agronomy","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/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/acc.2011.5991021","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2011.5991021","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2011 American Control Conference","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W19432330","https://openalex.org/W1484739396","https://openalex.org/W1501759952","https://openalex.org/W1543651123","https://openalex.org/W1972176790","https://openalex.org/W1989230227","https://openalex.org/W2040065642","https://openalex.org/W2046287268","https://openalex.org/W2090167557","https://openalex.org/W2099308299","https://openalex.org/W2099567135","https://openalex.org/W2100432436","https://openalex.org/W2102415323","https://openalex.org/W2102899117","https://openalex.org/W2104103836","https://openalex.org/W2104958104","https://openalex.org/W2107615213","https://openalex.org/W2116007368","https://openalex.org/W2118741873","https://openalex.org/W2119596529","https://openalex.org/W2127918239","https://openalex.org/W2128011079","https://openalex.org/W2129758865","https://openalex.org/W2136384363","https://openalex.org/W2145530662","https://openalex.org/W2162297159","https://openalex.org/W2561640728","https://openalex.org/W4239216443","https://openalex.org/W6600799268","https://openalex.org/W6682002933"],"related_works":["https://openalex.org/W3217133416","https://openalex.org/W2349796700","https://openalex.org/W1970635650","https://openalex.org/W2475132469","https://openalex.org/W2314968026","https://openalex.org/W1976574339","https://openalex.org/W2126112326","https://openalex.org/W4237316100","https://openalex.org/W2907038991","https://openalex.org/W4396237395"],"abstract_inverted_index":{"The":[0],"notion":[1],"of":[2,23,32,109,133,144],"synergistic":[3,48,53,73,92],"potential":[4,49],"functions":[5,50],"has":[6,14],"been":[7,15],"introduced":[8],"recently":[9],"in":[10],"the":[11,18,21,80,87,131,138],"literature":[12],"and":[13,45,76,94],"used":[16],"as":[17,42],"basis":[19],"for":[20,124,141],"design":[22],"hybrid":[24,101,114],"feedback":[25,77,95],"laws":[26],"that":[27],"achieve":[28],"global":[29],"asymptotic":[30],"stabilization":[31,143],"a":[33,36,71,91,107,118,145,149],"point":[34],"on":[35],"compact":[37],"manifold":[38],"(without":[39],"boundary)":[40],"such":[41],"S1,":[43],"S2,":[44],"SO(3).":[46],"Here,":[47],"are":[51,56],"generalized-to":[52],"Lyapunov":[54,74,93],"functions-and":[55],"shown":[57],"to":[58,61],"be":[59,122],"amenable":[60],"backstepping.":[62],"In":[63,111],"particular,":[64],"if":[65],"an":[66,83],"afflne":[67],"control":[68,115,125],"system":[69,81],"admits":[70,90],"(weak)":[72],"function":[75],"pair":[78],"then":[79],"with":[82],"integrator":[84],"added":[85],"at":[86,117],"input":[88],"also":[89],"pair.":[96],"This":[97],"fact":[98],"enables":[99],"\"smoothing\"":[100],"feedbacks,":[102],"or":[103,129],"implementing":[104],"them":[105],"through":[106,126],"chain":[108],"integrators.":[110],"this":[112],"way,":[113],"designed":[116],"kinematic":[119],"level":[120],"can":[121],"redesigned":[123],"forces,":[127],"torques,":[128],"even":[130],"derivative":[132],"these":[134],"quantities.":[135],"We":[136],"demonstrate":[137],"backstepping":[139],"procedure":[140],"attitude":[142],"rigid":[146],"body":[147],"using":[148],"quaternion":[150],"parametrization.":[151]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}