{"id":"https://openalex.org/W2793407447","doi":"https://doi.org/10.1109/tac.2018.2812789","title":"A Novel Method to Estimate the Reaching Time of the Super-Twisting Algorithm","display_name":"A Novel Method to Estimate the Reaching Time of the Super-Twisting Algorithm","publication_year":2018,"publication_date":"2018-03-06","ids":{"openalex":"https://openalex.org/W2793407447","doi":"https://doi.org/10.1109/tac.2018.2812789","mag":"2793407447"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2018.2812789","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2018.2812789","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":true,"oa_status":"green","oa_url":"http://openlib.tugraz.at/5cfed42c7822e","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5010534287","display_name":"Richard Seeber","orcid":"https://orcid.org/0000-0003-4430-5626"},"institutions":[{"id":"https://openalex.org/I4092182","display_name":"Graz University of Technology","ror":"https://ror.org/00d7xrm67","country_code":"AT","type":"education","lineage":["https://openalex.org/I4092182"]},{"id":"https://openalex.org/I8961855","display_name":"Universidad Nacional Aut\u00f3noma de M\u00e9xico","ror":"https://ror.org/01tmp8f25","country_code":"MX","type":"education","lineage":["https://openalex.org/I8961855"]}],"countries":["AT","MX"],"is_corresponding":false,"raw_author_name":"Richard Seeber","raw_affiliation_strings":["Christian Doppler Laboratory for Model Based Control of Complex Test Bed Systems, Graz University of Technology, Graz, Austria","Engineering Faculty, National Autonomous University of Mexico (UNAM), Ciudad Universitaria, Mexico;","Laboratory for Model Based Control of Complex Test Bed Systems, Institute of Automation and Control, Graz University of Technology, Graz, Austria;"],"raw_orcid":"https://orcid.org/0000-0003-4430-5626","affiliations":[{"raw_affiliation_string":"Christian Doppler Laboratory for Model Based Control of Complex Test Bed Systems, Graz University of Technology, Graz, Austria","institution_ids":["https://openalex.org/I4092182"]},{"raw_affiliation_string":"Engineering Faculty, National Autonomous University of Mexico (UNAM), Ciudad Universitaria, Mexico;","institution_ids":["https://openalex.org/I8961855"]},{"raw_affiliation_string":"Laboratory for Model Based Control of Complex Test Bed Systems, Institute of Automation and Control, Graz University of Technology, Graz, Austria;","institution_ids":["https://openalex.org/I4092182"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025122566","display_name":"Martin Horn","orcid":"https://orcid.org/0000-0002-5845-1061"},"institutions":[{"id":"https://openalex.org/I4092182","display_name":"Graz University of Technology","ror":"https://ror.org/00d7xrm67","country_code":"AT","type":"education","lineage":["https://openalex.org/I4092182"]},{"id":"https://openalex.org/I8961855","display_name":"Universidad Nacional Aut\u00f3noma de M\u00e9xico","ror":"https://ror.org/01tmp8f25","country_code":"MX","type":"education","lineage":["https://openalex.org/I8961855"]}],"countries":["AT","MX"],"is_corresponding":false,"raw_author_name":"Martin Horn","raw_affiliation_strings":["Christian Doppler Laboratory for Model Based Control of Complex Test Bed Systems, Graz University of Technology, Graz, Austria","Laboratory for Model Based Control of Complex Test Bed Systems, Institute of Automation and Control, Graz University of Technology, Graz, Austria;","Engineering Faculty, National Autonomous University of Mexico (UNAM), Ciudad Universitaria, Mexico;"],"raw_orcid":"https://orcid.org/0000-0002-5845-1061","affiliations":[{"raw_affiliation_string":"Christian Doppler Laboratory for Model Based Control of Complex Test Bed Systems, Graz University of Technology, Graz, Austria","institution_ids":["https://openalex.org/I4092182"]},{"raw_affiliation_string":"Laboratory for Model Based Control of Complex Test Bed Systems, Institute of Automation and Control, Graz University of Technology, Graz, Austria;","institution_ids":["https://openalex.org/I4092182"]},{"raw_affiliation_string":"Engineering Faculty, National Autonomous University of Mexico (UNAM), Ciudad Universitaria, Mexico;","institution_ids":["https://openalex.org/I8961855"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5032593897","display_name":"Leonid Fridman","orcid":"https://orcid.org/0000-0003-0208-3615"},"institutions":[{"id":"https://openalex.org/I167724894","display_name":"Universidad Aut\u00f3noma de la Ciudad de M\u00e9xico","ror":"https://ror.org/04q0r6m34","country_code":"MX","type":"education","lineage":["https://openalex.org/I167724894"]},{"id":"https://openalex.org/I4092182","display_name":"Graz University of Technology","ror":"https://ror.org/00d7xrm67","country_code":"AT","type":"education","lineage":["https://openalex.org/I4092182"]},{"id":"https://openalex.org/I8961855","display_name":"Universidad Nacional Aut\u00f3noma de M\u00e9xico","ror":"https://ror.org/01tmp8f25","country_code":"MX","type":"education","lineage":["https://openalex.org/I8961855"]}],"countries":["AT","MX"],"is_corresponding":false,"raw_author_name":"Leonid Fridman","raw_affiliation_strings":["Engineering Faculty, Ciudad Universitaria, Mexico City, Mexico","Laboratory for Model Based Control of Complex Test Bed Systems, Institute of Automation and Control, Graz University of Technology, Graz, Austria;","Engineering Faculty, National Autonomous University of Mexico (UNAM), Ciudad Universitaria, Mexico;"],"raw_orcid":"https://orcid.org/0000-0003-0208-3615","affiliations":[{"raw_affiliation_string":"Engineering Faculty, Ciudad Universitaria, Mexico City, Mexico","institution_ids":["https://openalex.org/I167724894"]},{"raw_affiliation_string":"Laboratory for Model Based Control of Complex Test Bed Systems, Institute of Automation and Control, Graz University of Technology, Graz, Austria;","institution_ids":["https://openalex.org/I4092182"]},{"raw_affiliation_string":"Engineering Faculty, National Autonomous University of Mexico (UNAM), Ciudad Universitaria, Mexico;","institution_ids":["https://openalex.org/I8961855"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.5657,"has_fulltext":true,"cited_by_count":98,"citation_normalized_percentile":{"value":0.96322773,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":100},"biblio":{"volume":"63","issue":"12","first_page":"4301","last_page":"4308"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"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"}},"topics":[{"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/T11236","display_name":"Control Systems and Identification","score":0.9937999844551086,"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/T11749","display_name":"Iterative Learning Control Systems","score":0.9901000261306763,"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/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.6637442708015442},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6175184845924377},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5834110379219055},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5485424399375916},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.5338788032531738},{"id":"https://openalex.org/keywords/sliding-mode-control","display_name":"Sliding mode control","score":0.5207716822624207},{"id":"https://openalex.org/keywords/expression","display_name":"Expression (computer science)","score":0.47064346075057983},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.41490232944488525},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.35734719038009644},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.2848912477493286},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.26711028814315796},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2660374343395233},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.09963807463645935},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07778593897819519}],"concepts":[{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.6637442708015442},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6175184845924377},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5834110379219055},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5485424399375916},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5338788032531738},{"id":"https://openalex.org/C36662352","wikidata":"https://www.wikidata.org/wiki/Q6008560","display_name":"Sliding mode control","level":3,"score":0.5207716822624207},{"id":"https://openalex.org/C90559484","wikidata":"https://www.wikidata.org/wiki/Q778379","display_name":"Expression (computer science)","level":2,"score":0.47064346075057983},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.41490232944488525},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.35734719038009644},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.2848912477493286},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.26711028814315796},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2660374343395233},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.09963807463645935},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07778593897819519},{"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},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tac.2018.2812789","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2018.2812789","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:http://openlib.tugraz.at/5cfed42c7822e","is_oa":true,"landing_page_url":"http://openlib.tugraz.at/5cfed42c7822e","pdf_url":"http://openlib.tugraz.at/5cfed42c7822e","source":{"id":"https://openalex.org/S4306400660","display_name":"TUGraz OPEN Library (Graz University of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4092182","host_organization_name":"Graz University of Technology","host_organization_lineage":["https://openalex.org/I4092182"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:http://openlib.tugraz.at/5cfed42c7822e","is_oa":true,"landing_page_url":"http://openlib.tugraz.at/5cfed42c7822e","pdf_url":"http://openlib.tugraz.at/5cfed42c7822e","source":{"id":"https://openalex.org/S4306400660","display_name":"TUGraz OPEN Library (Graz University of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4092182","host_organization_name":"Graz University of Technology","host_organization_lineage":["https://openalex.org/I4092182"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320310430","display_name":"TU Graz, Internationale Beziehungen und Mobilit\u00e4tsprogramme","ror":"https://ror.org/00d7xrm67"},{"id":"https://openalex.org/F4320311373","display_name":"International Foundation for Research in Experimental Economics","ror":"https://ror.org/00qcdw388"},{"id":"https://openalex.org/F4320311813","display_name":"\u00d6sterreichische Nationalstiftung f\u00fcr Forschung, Technologie und Entwicklung","ror":"https://ror.org/04hb33h70"},{"id":"https://openalex.org/F4320321896","display_name":"Bundesministerium f\u00fcr Wissenschaft, Forschung und Wirtschaft","ror":"https://ror.org/02d229b24"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2793407447.pdf","grobid_xml":"https://content.openalex.org/works/W2793407447.grobid-xml"},"referenced_works_count":19,"referenced_works":["https://openalex.org/W1580284638","https://openalex.org/W1592648094","https://openalex.org/W2018851823","https://openalex.org/W2023339343","https://openalex.org/W2030959268","https://openalex.org/W2031945217","https://openalex.org/W2036808929","https://openalex.org/W2078961016","https://openalex.org/W2099441579","https://openalex.org/W2103616988","https://openalex.org/W2124662518","https://openalex.org/W2164812525","https://openalex.org/W2420367108","https://openalex.org/W2474915920","https://openalex.org/W2571181456","https://openalex.org/W2618637859","https://openalex.org/W4237270139","https://openalex.org/W4293078920","https://openalex.org/W4294175419"],"related_works":["https://openalex.org/W3185235544","https://openalex.org/W2911623553","https://openalex.org/W4297791327","https://openalex.org/W2897842840","https://openalex.org/W2397777611","https://openalex.org/W1502031429","https://openalex.org/W2417585376","https://openalex.org/W1994157709","https://openalex.org/W4294336468","https://openalex.org/W2797811993"],"abstract_inverted_index":{"The":[0,57],"super-twisting":[1],"algorithm":[2],"is":[3,33,55,92],"a":[4,39],"well-known":[5],"technique":[6],"in":[7,29,71,76,83],"the":[8,30,43,47,51,77,84,89],"field":[9],"of":[10,46,53,63,86],"sliding":[11,78],"mode":[12],"control":[13],"or":[14,73],"observation.":[15],"In":[16],"this":[17,24,37],"contribution,":[18],"an":[19],"exact":[20],"analytic":[21],"expression":[22],"for":[23,42],"algorithm's":[25,48],"finite":[26],"reaching":[27,49,101],"time":[28,50,72,102],"unperturbed":[31],"case":[32],"derived.":[34],"Based":[35],"on":[36],"derivation,":[38],"novel":[40],"estimation":[41],"upper":[44],"bound":[45],"presence":[52],"perturbations":[54,59],"presented.":[56],"considered":[58],"may":[60],"be":[61],"composed":[62],"additive":[64],"components":[65],"that":[66],"are":[67],"either":[68],"Lipschitz":[69],"continuous":[70,75],"H\u00f6lder":[74],"variable.":[79],"Both":[80],"analytically":[81],"and":[82],"course":[85],"numerical":[87],"examples":[88],"new":[90],"strategy":[91],"shown":[93],"to":[94,99],"yield":[95],"significant":[96],"improvements":[97],"compared":[98],"existing":[100],"estimates.":[103]},"counts_by_year":[{"year":2026,"cited_by_count":6},{"year":2025,"cited_by_count":13},{"year":2024,"cited_by_count":16},{"year":2023,"cited_by_count":10},{"year":2022,"cited_by_count":15},{"year":2021,"cited_by_count":10},{"year":2020,"cited_by_count":12},{"year":2019,"cited_by_count":12},{"year":2018,"cited_by_count":4}],"updated_date":"2026-07-25T09:21:30.201066","created_date":"2025-10-10T00:00:00"}