{"id":"https://openalex.org/W2784008933","doi":"https://doi.org/10.1109/cdc.2017.8264462","title":"An idea for Lyapunov function design for arbitrary order continuous twisting algorithms","display_name":"An idea for Lyapunov function design for arbitrary order continuous twisting algorithms","publication_year":2017,"publication_date":"2017-12-01","ids":{"openalex":"https://openalex.org/W2784008933","doi":"https://doi.org/10.1109/cdc.2017.8264462","mag":"2784008933"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2017.8264462","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2017.8264462","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2017 IEEE 56th Annual Conference on Decision and Control (CDC)","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/A5063578435","display_name":"Jes\u00fas Mendoza\u2010Avila","orcid":"https://orcid.org/0000-0003-1374-4132"},"institutions":[{"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":["MX"],"is_corresponding":false,"raw_author_name":"Jesus Mendoza-Avila","raw_affiliation_strings":["Facultad de Ingenier\u00eda, Universidad Nacional Aut\u00f3noma de M\u00e9xico, Mexico City, Mexico"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Facultad de Ingenier\u00eda, Universidad Nacional Aut\u00f3noma de M\u00e9xico, Mexico City, Mexico","institution_ids":["https://openalex.org/I8961855"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011888247","display_name":"Jaime A. Moreno","orcid":"https://orcid.org/0000-0002-2556-9784"},"institutions":[{"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":["MX"],"is_corresponding":false,"raw_author_name":"Jaime A. Moreno","raw_affiliation_strings":["Instituto de Ingenier\u00eda, Universidad Nacional Aut\u00f3noma de M\u00e9xico, Mexico City, Mexico"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Instituto de Ingenier\u00eda, Universidad Nacional Aut\u00f3noma de M\u00e9xico, Mexico City, 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/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":["MX"],"is_corresponding":false,"raw_author_name":"Leonid Fridman","raw_affiliation_strings":["Institut f\u00fcr Regelungs und Automatisierungstechnik, Universidad Nacional Aut\u00f3noma de M\u00e9xico, Mexico City, Mexico"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Regelungs und Automatisierungstechnik, Universidad Nacional Aut\u00f3noma de M\u00e9xico, Mexico City, Mexico","institution_ids":["https://openalex.org/I8961855"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I8961855"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":"28","issue":null,"first_page":"5426","last_page":"5431"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10040","display_name":"Adaptive Control of Nonlinear Systems","score":0.9991999864578247,"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":0.9991999864578247,"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/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.9962000250816345,"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/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.9936000108718872,"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":0.6091493368148804},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.5399467945098877},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.5312763452529907},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5202195048332214},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.49524274468421936},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.49197885394096375},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.47955939173698425},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4573156535625458},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4398321807384491},{"id":"https://openalex.org/keywords/sliding-mode-control","display_name":"Sliding mode control","score":0.4114110469818115},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3459494113922119},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.33050477504730225},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.20554310083389282},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.2005113661289215},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.06981968879699707}],"concepts":[{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.6091493368148804},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.5399467945098877},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5312763452529907},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5202195048332214},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.49524274468421936},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.49197885394096375},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.47955939173698425},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4573156535625458},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4398321807384491},{"id":"https://openalex.org/C36662352","wikidata":"https://www.wikidata.org/wiki/Q6008560","display_name":"Sliding mode control","level":3,"score":0.4114110469818115},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3459494113922119},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.33050477504730225},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.20554310083389282},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.2005113661289215},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.06981968879699707},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cdc.2017.8264462","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2017.8264462","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2017 IEEE 56th Annual Conference on Decision and Control (CDC)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W1516289514","https://openalex.org/W1516447630","https://openalex.org/W1552510372","https://openalex.org/W1999558720","https://openalex.org/W2077537048","https://openalex.org/W2106850246","https://openalex.org/W2113766349","https://openalex.org/W2133404041","https://openalex.org/W2158503284","https://openalex.org/W2205284724","https://openalex.org/W2208608249","https://openalex.org/W2289781353","https://openalex.org/W2305138675","https://openalex.org/W2563369907","https://openalex.org/W2587895662","https://openalex.org/W2599070313","https://openalex.org/W2963045434","https://openalex.org/W2971246051","https://openalex.org/W4256152864","https://openalex.org/W4256153703","https://openalex.org/W4293738473","https://openalex.org/W6687733127"],"related_works":["https://openalex.org/W3185235544","https://openalex.org/W4297791327","https://openalex.org/W2897842840","https://openalex.org/W2911623553","https://openalex.org/W2397777611","https://openalex.org/W1502031429","https://openalex.org/W2318923278","https://openalex.org/W2417585376","https://openalex.org/W1994157709","https://openalex.org/W2797811993"],"abstract_inverted_index":{"Continuous":[0],"Twisting":[1],"Algorithm":[2],"(CTA)":[3],"for":[4,44,51,67,89,102,141,159],"systems":[5,162],"of":[6,30,40,77,82,96,104,136,156],"order":[7,31,55,72,97,105,144,161],"n":[8,52,69],"allows":[9,150],"to":[10,26,151,164],"compensate":[11],"theoretically":[12],"exactly":[13],"Lipschitz":[14],"time":[15],"perturbations,":[16],"generating":[17],"a":[18,27,41,64,75,87,100,125,137],"continuous":[19,91],"control":[20,154],"signal":[21],"and":[22,48,109,139,163],"ensuring":[23],"finite-time":[24,167],"convergence":[25],"sliding":[28],"mode":[29],"(n":[32,106],"+":[33],"1).":[34],"In":[35],"this":[36],"paper":[37],"an":[38],"idea":[39,130],"recursive":[42,126],"procedure":[43,60,149],"Lypaunov":[45],"Function":[46],"(LF)":[47],"gains":[49,140,155],"design":[50,135],"-":[53,70,107],"th":[54,71],"CTA":[56,73,103,158],"is":[57,131],"proposed.":[58],"The":[59,115,128],"consists":[61],"in":[62,120,124],"constructing":[63],"homogeneous":[65,80],"LF":[66,88,101,138],"the":[68,83,90,134,142,147,153,157],"as":[74],"sum":[76],"three":[78],"generalized":[79],"polynomials":[81],"same":[84],"degree:":[85],"(i)":[86],"state":[92],"feedback":[93],"controlled":[94],"system":[95],"n;":[98],"(ii)":[99],"1)":[108],"(iii)":[110],"some":[111],"extra":[112],"cross":[113],"terms.":[114],"two":[116],"first":[117],"terms":[118],"can":[119],"turn":[121],"be":[122],"constructed":[123],"form.":[127],"proposed":[129,148],"illustrated":[132],"with":[133],"second":[143],"CTA.":[145],"Furthermore,":[146],"select":[152],"third":[160],"prove":[165],"global":[166],"stability.":[168]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":3}],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}