{"id":"https://openalex.org/W2793715461","doi":"https://doi.org/10.1109/tac.2018.2794411","title":"A Lyapunov Function for an Extended Super-Twisting Algorithm","display_name":"A Lyapunov Function for an Extended Super-Twisting Algorithm","publication_year":2018,"publication_date":"2018-01-19","ids":{"openalex":"https://openalex.org/W2793715461","doi":"https://doi.org/10.1109/tac.2018.2794411","mag":"2793715461"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2018.2794411","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2018.2794411","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/5cfed4286ed83","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"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"Richard Seeber","raw_affiliation_strings":["Christian Doppler Laboratory for Model Based Control of Complex Test Bed Systems, Institute of Automation and Control, Graz University of Technology, Graz, Austria","Model Based Control of Complex Test Bed Systems, Institute for Automation and Control, Graz University of Technology, Graz, Austria;"],"affiliations":[{"raw_affiliation_string":"Christian Doppler 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":"Model Based Control of Complex Test Bed Systems, Institute for Automation and Control, Graz University of Technology, Graz, Austria;","institution_ids":["https://openalex.org/I4092182"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5032824476","display_name":"Markus Reichhartinger","orcid":"https://orcid.org/0000-0003-4681-9575"},"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"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Markus Reichhartinger","raw_affiliation_strings":["Christian Doppler Laboratory for Model Based Control of Complex Test Bed Systems, Institute of Automation and Control, Graz University of Technology, Graz, Austria","Model Based Control of Complex Test Bed Systems, Institute for Automation and Control, Graz University of Technology, Graz, Austria;"],"affiliations":[{"raw_affiliation_string":"Christian Doppler 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":"Model Based Control of Complex Test Bed Systems, Institute for Automation and Control, Graz University of Technology, Graz, Austria;","institution_ids":["https://openalex.org/I4092182"]}]},{"author_position":"last","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"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Martin Horn","raw_affiliation_strings":["Christian Doppler Laboratory for Model Based Control of Complex Test Bed Systems, Institute of Automation and Control, Graz University of Technology, Graz, Austria","Model Based Control of Complex Test Bed Systems, Institute for Automation and Control, Graz University of Technology, Graz, Austria;"],"affiliations":[{"raw_affiliation_string":"Christian Doppler 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":"Model Based Control of Complex Test Bed Systems, Institute for Automation and Control, Graz University of Technology, Graz, Austria;","institution_ids":["https://openalex.org/I4092182"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5010534287"],"corresponding_institution_ids":["https://openalex.org/I4092182"],"apc_list":null,"apc_paid":null,"fwci":2.0598,"has_fulltext":false,"cited_by_count":21,"citation_normalized_percentile":{"value":0.8722175,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"63","issue":"10","first_page":"3426","last_page":"3433"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10040","display_name":"Adaptive Control of Nonlinear Systems","score":0.9979000091552734,"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":0.9979000091552734,"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":0.9882000088691711,"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"}},{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9882000088691711,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.7644929885864258},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6857254505157471},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.520179271697998},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5063036680221558},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4831685423851013},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.45752251148223877},{"id":"https://openalex.org/keywords/lyapunov-equation","display_name":"Lyapunov equation","score":0.43207627534866333},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.41090357303619385},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4080265760421753},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.35960108041763306},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.17566096782684326}],"concepts":[{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.7644929885864258},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6857254505157471},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.520179271697998},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5063036680221558},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4831685423851013},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.45752251148223877},{"id":"https://openalex.org/C25854792","wikidata":"https://www.wikidata.org/wiki/Q1028945","display_name":"Lyapunov equation","level":4,"score":0.43207627534866333},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.41090357303619385},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4080265760421753},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35960108041763306},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.17566096782684326},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tac.2018.2794411","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2018.2794411","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/5cfed4286ed83","is_oa":true,"landing_page_url":"http://openlib.tugraz.at/5cfed4286ed83","pdf_url":null,"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":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"","raw_type":null}],"best_oa_location":{"id":"pmh:http://openlib.tugraz.at/5cfed4286ed83","is_oa":true,"landing_page_url":"http://openlib.tugraz.at/5cfed4286ed83","pdf_url":null,"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":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"","raw_type":null},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W747566313","https://openalex.org/W1496537269","https://openalex.org/W1592648094","https://openalex.org/W1967073510","https://openalex.org/W1999558720","https://openalex.org/W2001721683","https://openalex.org/W2003880081","https://openalex.org/W2018851823","https://openalex.org/W2030230337","https://openalex.org/W2031945217","https://openalex.org/W2062563267","https://openalex.org/W2091198516","https://openalex.org/W2097032197","https://openalex.org/W2111018365","https://openalex.org/W2133404041","https://openalex.org/W2146586176","https://openalex.org/W2154608673","https://openalex.org/W2265937691","https://openalex.org/W2305138675","https://openalex.org/W2536620281","https://openalex.org/W2587895662","https://openalex.org/W2599070313","https://openalex.org/W2963045434","https://openalex.org/W2971246051","https://openalex.org/W4231266544","https://openalex.org/W4253577938","https://openalex.org/W4293078920","https://openalex.org/W6679392325"],"related_works":["https://openalex.org/W2349796700","https://openalex.org/W2383986032","https://openalex.org/W2030955003","https://openalex.org/W2374426356","https://openalex.org/W1977987201","https://openalex.org/W2059628530","https://openalex.org/W2164487476","https://openalex.org/W3194517843","https://openalex.org/W2106169668","https://openalex.org/W2534107666"],"abstract_inverted_index":{"Recently,":[0],"an":[1],"extension":[2],"of":[3,21,35,40,52,64,85,95,113,126,134],"the":[4,33,41,73,81,86,114,124,135],"super-twisting":[5],"algorithm":[6,28],"for":[7,26,44,137],"relative":[8],"degrees":[9],"<inline-formula":[10,45,138],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[11,46,139],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">":[12],"<tex-math":[13],"notation=\"LaTeX\">$m\\geq":[14],"{}1$</tex-math></inline-formula>":[15],"has":[16],"been":[17],"proposed.":[18,130],"However,":[19],"as":[20,105],"yet,":[22],"no":[23],"Lyapunov":[24,36,54,74,103],"functions":[25,37],"this":[27,96,109],"exist.":[29],"This":[30],"paper":[31],"discusses":[32],"construction":[34],"by":[38],"means":[39],"sum-of-squares":[42],"technique":[43],"xmlns:xlink=\"http://www.w3.org/1999/xlink\"><tex-math":[47,140],"notation=\"LaTeX\">$m=1$</tex-math></inline-formula>":[48],".":[49],"Sign":[50],"definiteness":[51],"both":[53],"function":[55,75,98,104],"and":[56,121],"its":[57],"time":[58,83],"derivative":[59],"is":[60,90,129,143],"shown":[61],"in":[62,123],"spite":[63],"numerically":[65],"obtained\u2014and":[66],"hence":[67],"possibly":[68],"inexact\u2014sum-of-squares":[69],"decompositions.":[70],"By":[71],"choosing":[72],"to":[76],"be":[77],"a":[78,100,111,132],"positive":[79,101],"semidefinite,":[80],"finite":[82],"attractivity":[84],"system's":[87],"multiple":[88],"equilibria":[89],"shown.":[91],"A":[92],"simple":[93],"modification":[94],"semidefinite":[97],"yields":[99],"definite":[102],"well.":[106],"Based":[107],"on":[108],"approach,":[110],"set":[112],"algorithm's":[115],"tuning":[116],"parameters":[117],"ensuring":[118],"finite-time":[119],"convergence":[120],"stability":[122],"presence":[125],"bounded":[127],"uncertainties":[128],"Finally,":[131],"generalization":[133],"approach":[136],"notation=\"LaTeX\">":[141],"$m&gt;1$</tex-math></inline-formula>":[142],"outlined.":[144]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":3}],"updated_date":"2026-04-18T07:56:08.524223","created_date":"2025-10-10T00:00:00"}
