{"id":"https://openalex.org/W2171879251","doi":"https://doi.org/10.1109/tac.2014.2299335","title":"Rapidly Exponentially Stabilizing Control Lyapunov Functions and Hybrid Zero Dynamics","display_name":"Rapidly Exponentially Stabilizing Control Lyapunov Functions and Hybrid Zero Dynamics","publication_year":2014,"publication_date":"2014-01-31","ids":{"openalex":"https://openalex.org/W2171879251","doi":"https://doi.org/10.1109/tac.2014.2299335","mag":"2171879251"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2014.2299335","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2014.2299335","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","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://figshare.com/articles/journal_contribution/Rapidly_Exponentially_Stabilizing_Control_Lyapunov_Functions_and_Hybrid_Zero_Dynamics/6490121","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5039171820","display_name":"Aaron D. Ames","orcid":"https://orcid.org/0000-0003-0848-3177"},"institutions":[{"id":"https://openalex.org/I91045830","display_name":"Texas A&M University","ror":"https://ror.org/01f5ytq51","country_code":"US","type":"education","lineage":["https://openalex.org/I91045830"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Aaron D. Ames","raw_affiliation_strings":["Department of Mechanical Engineering, Texas A&M University, College Station, TX, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, Texas A&M University, College Station, TX, USA","institution_ids":["https://openalex.org/I91045830"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036845309","display_name":"Kevin S. Galloway","orcid":"https://orcid.org/0000-0001-5604-6815"},"institutions":[{"id":"https://openalex.org/I189158971","display_name":"United States Naval Academy","ror":"https://ror.org/00znex860","country_code":"US","type":"education","lineage":["https://openalex.org/I1330347796","https://openalex.org/I189158971","https://openalex.org/I3130687028"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Kevin Galloway","raw_affiliation_strings":["United States Naval Academy, Electrical and Computer Engineering Department, Annapolis, MD, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"United States Naval Academy, Electrical and Computer Engineering Department, Annapolis, MD, USA","institution_ids":["https://openalex.org/I189158971"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054075105","display_name":"Koushil Sreenath","orcid":"https://orcid.org/0000-0002-5346-3637"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Koushil Sreenath","raw_affiliation_strings":["Departments of Mechanical Engineering and Robotics Institute, Carnegie Mellon University, Pittsburgh, PA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departments of Mechanical Engineering and Robotics Institute, Carnegie Mellon University, Pittsburgh, PA, USA","institution_ids":["https://openalex.org/I74973139"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5037697344","display_name":"Jessy W. Grizzle","orcid":"https://orcid.org/0000-0001-7586-0142"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jessy W. Grizzle","raw_affiliation_strings":["Electrical Engineering and Computer Science Department, Control Systems Laboratory, Ann Arbor, MI, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Electrical Engineering and Computer Science Department, Control Systems Laboratory, Ann Arbor, MI, USA","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":15.1147,"has_fulltext":false,"cited_by_count":452,"citation_normalized_percentile":{"value":0.99512664,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"59","issue":"4","first_page":"876","last_page":"891"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10879","display_name":"Robotic Locomotion and Control","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical 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/T10879","display_name":"Robotic Locomotion and Control","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical 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/T11023","display_name":"Prosthetics and Rehabilitation Robotics","score":0.9894999861717224,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical 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/T12400","display_name":"Neurogenetic and Muscular Disorders Research","score":0.9858999848365784,"subfield":{"id":"https://openalex.org/subfields/2716","display_name":"Genetics"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.686458945274353},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.6569613814353943},{"id":"https://openalex.org/keywords/exponential-stability","display_name":"Exponential stability","score":0.5821542143821716},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5677440166473389},{"id":"https://openalex.org/keywords/linearization","display_name":"Linearization","score":0.4305751919746399},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2200489640235901},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.15660494565963745},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.10927525162696838},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.09594792127609253}],"concepts":[{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.686458945274353},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.6569613814353943},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.5821542143821716},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5677440166473389},{"id":"https://openalex.org/C11210021","wikidata":"https://www.wikidata.org/wiki/Q1520713","display_name":"Linearization","level":3,"score":0.4305751919746399},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2200489640235901},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.15660494565963745},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.10927525162696838},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.09594792127609253},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","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":5,"locations":[{"id":"doi:10.1109/tac.2014.2299335","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2014.2299335","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:10.1.1.299.2098","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.299.2098","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://web.eecs.umich.edu/~grizzle/papers/CFL_Robotics_2012TAC.pdf","raw_type":"text"},{"id":"pmh:oai:repository.cmu.edu:meche-1139","is_oa":false,"landing_page_url":"http://repository.cmu.edu/cgi/viewcontent.cgi?article=1139&context=meche","pdf_url":null,"source":{"id":"https://openalex.org/S7407050927","display_name":"KiltHub Repository","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I74973139","host_organization_name":"Carnegie Mellon University","host_organization_lineage":["https://openalex.org/I74973139"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Department of Mechanical Engineering","raw_type":"text"},{"id":"pmh:oai:figshare.com:article/6490121","is_oa":true,"landing_page_url":"https://figshare.com/articles/journal_contribution/Rapidly_Exponentially_Stabilizing_Control_Lyapunov_Functions_and_Hybrid_Zero_Dynamics/6490121","pdf_url":null,"source":{"id":"https://openalex.org/S4306402621","display_name":"INDIGO (University of Illinois at Chicago)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I39422238","host_organization_name":"University of Illinois Chicago","host_organization_lineage":["https://openalex.org/I39422238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"doi:10.1184/r1/6490121.v1","is_oa":true,"landing_page_url":"https://doi.org/10.1184/r1/6490121.v1","pdf_url":null,"source":{"id":"https://openalex.org/S7407050927","display_name":"KiltHub Repository","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I74973139","host_organization_name":"Carnegie Mellon University","host_organization_lineage":["https://openalex.org/I74973139"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"JournalArticle"}],"best_oa_location":{"id":"pmh:oai:figshare.com:article/6490121","is_oa":true,"landing_page_url":"https://figshare.com/articles/journal_contribution/Rapidly_Exponentially_Stabilizing_Control_Lyapunov_Functions_and_Hybrid_Zero_Dynamics/6490121","pdf_url":null,"source":{"id":"https://openalex.org/S4306402621","display_name":"INDIGO (University of Illinois at Chicago)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I39422238","host_organization_name":"University of Illinois Chicago","host_organization_lineage":["https://openalex.org/I39422238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":62,"referenced_works":["https://openalex.org/W83782864","https://openalex.org/W111272207","https://openalex.org/W120243950","https://openalex.org/W567663339","https://openalex.org/W1484739396","https://openalex.org/W1496537269","https://openalex.org/W1499219562","https://openalex.org/W1504362584","https://openalex.org/W1515569264","https://openalex.org/W1524096630","https://openalex.org/W1531111427","https://openalex.org/W1548148540","https://openalex.org/W1561445488","https://openalex.org/W1880805667","https://openalex.org/W1887006513","https://openalex.org/W1966972652","https://openalex.org/W1986164962","https://openalex.org/W1993314711","https://openalex.org/W2023126268","https://openalex.org/W2023285936","https://openalex.org/W2025135845","https://openalex.org/W2026616272","https://openalex.org/W2030515455","https://openalex.org/W2041076275","https://openalex.org/W2055728085","https://openalex.org/W2070924546","https://openalex.org/W2075546205","https://openalex.org/W2079407617","https://openalex.org/W2090167557","https://openalex.org/W2099308299","https://openalex.org/W2106985815","https://openalex.org/W2122116594","https://openalex.org/W2122171303","https://openalex.org/W2128131727","https://openalex.org/W2128198426","https://openalex.org/W2128592712","https://openalex.org/W2132347660","https://openalex.org/W2133582863","https://openalex.org/W2134078068","https://openalex.org/W2136605942","https://openalex.org/W2137547873","https://openalex.org/W2140531311","https://openalex.org/W2140795564","https://openalex.org/W2149224990","https://openalex.org/W2155658243","https://openalex.org/W2157924809","https://openalex.org/W2159635707","https://openalex.org/W2162053828","https://openalex.org/W2162193912","https://openalex.org/W2165626406","https://openalex.org/W2171729714","https://openalex.org/W2174809691","https://openalex.org/W2231168383","https://openalex.org/W2236379170","https://openalex.org/W2381269752","https://openalex.org/W2566720177","https://openalex.org/W2951886797","https://openalex.org/W3160954918","https://openalex.org/W3201048512","https://openalex.org/W4292872153","https://openalex.org/W6604981266","https://openalex.org/W6709612855"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2164703465","https://openalex.org/W2168383058","https://openalex.org/W2143247663","https://openalex.org/W2050693590"],"abstract_inverted_index":{"This":[0],"paper":[1,119],"addresses":[2],"the":[3,38,50,55,61,75,82,91,95,106,110,134,147,151,157],"problem":[4],"of":[5,14,41,84,94,105,117,124,146,159,171],"exponentially":[6,72],"stabilizing":[7,160],"periodic":[8,24,86,148],"orbits":[9,87],"in":[10,30,37,150],"a":[11,31,122,168,172],"special":[12],"class":[13,158],"hybrid":[15,62,76,169],"models-systems":[16],"with":[17,88,97],"impulse":[18,98],"effects-through":[19],"control":[20,125,187],"Lyapunov":[21,126,188],"functions.":[22,189],"The":[23,65,114,162],"orbit":[25,66,149],"is":[26,35,46,67,165,179],"assumed":[27,69],"to":[28,70,90,109,133,142,181],"lie":[29],"C1submanifold":[32],"Z":[33],"that":[34,121,128],"contained":[36],"zero":[39,63,77,111,135],"set":[40],"an":[42],"output":[43],"function":[44],"and":[45,52,178],"invariant":[47],"under":[48],"both":[49],"continuous":[51],"discrete":[53],"dynamics;":[54],"associated":[56],"restriction":[57],"dynamics":[58,93,107,112,136],"are":[59],"termed":[60],"dynamics.":[64,78],"furthermore":[68],"be":[71,140],"stable":[73],"within":[74],"Prior":[79],"results":[80],"on":[81,102,167],"stabilization":[83],"such":[85],"respect":[89],"full-order":[92,152],"system":[96],"effects":[99],"have":[100],"relied":[101],"input-output":[103],"linearization":[104],"transverse":[108],"manifold.":[113],"principal":[115],"result":[116,164],"this":[118],"demonstrates":[120],"variant":[123],"functions":[127],"enforce":[129],"rapid":[130],"exponential":[131,144],"convergence":[132],"surface,":[137],"Z,":[138],"can":[139],"used":[141],"achieve":[143,183],"stability":[145],"dynamics,":[153],"thereby":[154],"significantly":[155],"extending":[156],"controllers.":[161],"main":[163],"illustrated":[166],"model":[170],"bipedal":[173,184],"walking":[174],"robot":[175],"through":[176],"simulations":[177],"utilized":[180],"experimentally":[182],"locomotion":[185],"via":[186]},"counts_by_year":[{"year":2026,"cited_by_count":17},{"year":2025,"cited_by_count":36},{"year":2024,"cited_by_count":34},{"year":2023,"cited_by_count":39},{"year":2022,"cited_by_count":42},{"year":2021,"cited_by_count":59},{"year":2020,"cited_by_count":63},{"year":2019,"cited_by_count":47},{"year":2018,"cited_by_count":21},{"year":2017,"cited_by_count":27},{"year":2016,"cited_by_count":28},{"year":2015,"cited_by_count":27},{"year":2014,"cited_by_count":10},{"year":2013,"cited_by_count":2}],"updated_date":"2026-08-15T07:11:24.734988","created_date":"2025-10-10T00:00:00"}
