{"id":"https://openalex.org/W2591988490","doi":"https://doi.org/10.1080/00207179.2017.1295319","title":"The detection and stabilisation of limit cycle for deterministic finite automata","display_name":"The detection and stabilisation of limit cycle for deterministic finite automata","publication_year":2017,"publication_date":"2017-03-06","ids":{"openalex":"https://openalex.org/W2591988490","doi":"https://doi.org/10.1080/00207179.2017.1295319","mag":"2591988490"},"language":"en","primary_location":{"id":"doi:10.1080/00207179.2017.1295319","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207179.2017.1295319","pdf_url":null,"source":{"id":"https://openalex.org/S88061139","display_name":"International Journal of Control","issn_l":"0020-7179","issn":["0020-7179","1366-5820"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Control","raw_type":"journal-article"},"type":"article","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/A5081098250","display_name":"Xiaoguang Han","orcid":"https://orcid.org/0000-0003-0810-259X"},"institutions":[{"id":"https://openalex.org/I205237279","display_name":"Nankai University","ror":"https://ror.org/01y1kjr75","country_code":"CN","type":"education","lineage":["https://openalex.org/I205237279"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaoguang Han","raw_affiliation_strings":["College of Computer and Control Engineering, Nankai University, Tianjin, P. R. China","Tianjin Key Laboratory of Intelligent Robotics, Nankai University, Tianjin, P. R. China"],"raw_orcid":"https://orcid.org/0000-0003-0810-259X","affiliations":[{"raw_affiliation_string":"College of Computer and Control Engineering, Nankai University, Tianjin, P. R. China","institution_ids":["https://openalex.org/I205237279"]},{"raw_affiliation_string":"Tianjin Key Laboratory of Intelligent Robotics, Nankai University, Tianjin, P. R. China","institution_ids":["https://openalex.org/I205237279"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073105796","display_name":"Zengqiang Chen","orcid":null},"institutions":[{"id":"https://openalex.org/I205237279","display_name":"Nankai University","ror":"https://ror.org/01y1kjr75","country_code":"CN","type":"education","lineage":["https://openalex.org/I205237279"]},{"id":"https://openalex.org/I28813325","display_name":"Civil Aviation University of China","ror":"https://ror.org/03je71k37","country_code":"CN","type":"education","lineage":["https://openalex.org/I28813325"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Zengqiang Chen","raw_affiliation_strings":["College of Computer and Control Engineering, Nankai University, Tianjin, P. R. China","College of Science, Civil Aviation University of China, Tianjin, P. R. China","Tianjin Key Laboratory of Intelligent Robotics, Nankai University, Tianjin, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Computer and Control Engineering, Nankai University, Tianjin, P. R. China","institution_ids":["https://openalex.org/I205237279"]},{"raw_affiliation_string":"College of Science, Civil Aviation University of China, Tianjin, P. R. China","institution_ids":["https://openalex.org/I28813325"]},{"raw_affiliation_string":"Tianjin Key Laboratory of Intelligent Robotics, Nankai University, Tianjin, P. R. China","institution_ids":["https://openalex.org/I205237279"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5019147450","display_name":"Zhongxin Liu","orcid":"https://orcid.org/0000-0002-3565-4800"},"institutions":[{"id":"https://openalex.org/I205237279","display_name":"Nankai University","ror":"https://ror.org/01y1kjr75","country_code":"CN","type":"education","lineage":["https://openalex.org/I205237279"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhongxin Liu","raw_affiliation_strings":["College of Computer and Control Engineering, Nankai University, Tianjin, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Computer and Control Engineering, Nankai University, Tianjin, P. R. China","institution_ids":["https://openalex.org/I205237279"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100615838","display_name":"Qing Zhang","orcid":"https://orcid.org/0000-0003-3941-4764"},"institutions":[{"id":"https://openalex.org/I28813325","display_name":"Civil Aviation University of China","ror":"https://ror.org/03je71k37","country_code":"CN","type":"education","lineage":["https://openalex.org/I28813325"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qing Zhang","raw_affiliation_strings":["College of Science, Civil Aviation University of China, Tianjin, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Science, Civil Aviation University of China, Tianjin, P. R. China","institution_ids":["https://openalex.org/I28813325"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5073105796"],"corresponding_institution_ids":["https://openalex.org/I205237279","https://openalex.org/I28813325"],"apc_list":null,"apc_paid":null,"fwci":1.9124,"has_fulltext":false,"cited_by_count":26,"citation_normalized_percentile":{"value":0.8691501,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"91","issue":"4","first_page":"874","last_page":"886"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11125","display_name":"Petri Nets in System Modeling","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10904","display_name":"Embedded Systems Design Techniques","score":0.9922000169754028,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/limit-cycle","display_name":"Limit cycle","score":0.8024736642837524},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6865607500076294},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.6691155433654785},{"id":"https://openalex.org/keywords/deterministic-finite-automaton","display_name":"Deterministic finite automaton","score":0.6028354167938232},{"id":"https://openalex.org/keywords/limit-set","display_name":"Limit set","score":0.5863523483276367},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5256052017211914},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.5231360793113708},{"id":"https://openalex.org/keywords/automaton","display_name":"Automaton","score":0.4903726577758789},{"id":"https://openalex.org/keywords/tensor-product","display_name":"Tensor product","score":0.4884573519229889},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.46577781438827515},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4130590558052063},{"id":"https://openalex.org/keywords/finite-state-machine","display_name":"Finite-state machine","score":0.40910667181015015},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.34276682138442993},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.33325016498565674},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.24565187096595764},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.22499728202819824},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.18364524841308594},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.15234825015068054},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.14955952763557434}],"concepts":[{"id":"https://openalex.org/C93357160","wikidata":"https://www.wikidata.org/wiki/Q1545916","display_name":"Limit cycle","level":3,"score":0.8024736642837524},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6865607500076294},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.6691155433654785},{"id":"https://openalex.org/C104091681","wikidata":"https://www.wikidata.org/wiki/Q837528","display_name":"Deterministic finite automaton","level":3,"score":0.6028354167938232},{"id":"https://openalex.org/C51337361","wikidata":"https://www.wikidata.org/wiki/Q1825444","display_name":"Limit set","level":3,"score":0.5863523483276367},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5256052017211914},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.5231360793113708},{"id":"https://openalex.org/C112505250","wikidata":"https://www.wikidata.org/wiki/Q787116","display_name":"Automaton","level":2,"score":0.4903726577758789},{"id":"https://openalex.org/C51255310","wikidata":"https://www.wikidata.org/wiki/Q1163016","display_name":"Tensor product","level":2,"score":0.4884573519229889},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.46577781438827515},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4130590558052063},{"id":"https://openalex.org/C167822520","wikidata":"https://www.wikidata.org/wiki/Q176452","display_name":"Finite-state machine","level":2,"score":0.40910667181015015},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.34276682138442993},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.33325016498565674},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.24565187096595764},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.22499728202819824},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.18364524841308594},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.15234825015068054},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.14955952763557434},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207179.2017.1295319","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207179.2017.1295319","pdf_url":null,"source":{"id":"https://openalex.org/S88061139","display_name":"International Journal of Control","issn_l":"0020-7179","issn":["0020-7179","1366-5820"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Control","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3587069573","display_name":null,"funder_award_id":"61573199, 61573200","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G368305465","display_name":null,"funder_award_id":"14JCYBJC18700, 13JCYBJC17400","funder_id":"https://openalex.org/F4320323993","funder_display_name":"Natural Science Foundation of Tianjin City"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320323993","display_name":"Natural Science Foundation of Tianjin City","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W567151721","https://openalex.org/W1420949357","https://openalex.org/W1543281322","https://openalex.org/W1971318969","https://openalex.org/W1976432308","https://openalex.org/W1988926301","https://openalex.org/W1991079360","https://openalex.org/W1991720013","https://openalex.org/W1998083885","https://openalex.org/W2008831431","https://openalex.org/W2056372293","https://openalex.org/W2058188212","https://openalex.org/W2059057465","https://openalex.org/W2062325135","https://openalex.org/W2072382350","https://openalex.org/W2072471271","https://openalex.org/W2072890688","https://openalex.org/W2073458555","https://openalex.org/W2079042739","https://openalex.org/W2090408760","https://openalex.org/W2094700336","https://openalex.org/W2117011945","https://openalex.org/W2129231075","https://openalex.org/W2132980130","https://openalex.org/W2136433622","https://openalex.org/W2150577938","https://openalex.org/W2153400879","https://openalex.org/W2169597155","https://openalex.org/W2214188879","https://openalex.org/W2344696827","https://openalex.org/W2344793144","https://openalex.org/W4230297697","https://openalex.org/W4249866328","https://openalex.org/W4292003697"],"related_works":["https://openalex.org/W2355522437","https://openalex.org/W1428391281","https://openalex.org/W2111868903","https://openalex.org/W4281261571","https://openalex.org/W3087272834","https://openalex.org/W2280116234","https://openalex.org/W2146605784","https://openalex.org/W2384360959","https://openalex.org/W4252918107","https://openalex.org/W2591988490"],"abstract_inverted_index":{"In":[0],"this":[1,46],"paper,":[2],"the":[3,13,16,24,49,53,79,100,107,135,149,167,175,182,193],"topological":[4],"structure":[5],"properties":[6],"of":[7,15,19,26,42,51,56,69,71,85,88,90,118,130,137],"deterministic":[8],"finite":[9,128],"automata":[10],"(DFA),":[11],"under":[12],"framework":[14],"semi-tensor":[17],"product":[18],"matrices,":[20],"are":[21,28,159,178],"investigated.":[22],"First,":[23],"dynamics":[25],"DFA":[27,120,140],"converted":[29],"into":[30],"a":[31,36,91,119,122,127,139,145],"new":[32],"algebraic":[33,47],"form":[34],"as":[35],"discrete-time":[37],"linear":[38],"system":[39],"by":[40,148,180],"means":[41],"Boolean":[43],"algebra.":[44],"Using":[45],"description,":[48],"approach":[50],"calculating":[52,86],"limit":[54,72,92,103,124,146,157,176],"cycles":[55],"different":[57],"lengths":[58],"is":[59,94,132,153,189],"given.":[60,133],"Second,":[61],"we":[62,98],"present":[63],"two":[64],"fundamental":[65],"concepts,":[66],"namely,":[67],"domain":[68,87],"attraction":[70,89],"cycle":[73,93,125,147,177],"and":[74,105,109],"prereachability":[75,80],"set.":[76],"Based":[77],"on":[78],"set,":[81],"an":[82,186],"explicit":[83],"solution":[84],"completely":[95],"characterised.":[96],"Third,":[97],"define":[99],"globally":[101],"attractive":[102],"cycle,":[104],"then":[106],"necessary":[108],"sufficient":[110],"condition":[111],"for":[112,156],"verifying":[113],"whether":[114,138],"all":[115],"state":[116,150,162,173],"trajectories":[117,170],"enter":[121],"given":[123],"in":[126],"number":[129],"transitions":[131],"Fourth,":[134],"problem":[136],"can":[141],"be":[142],"stabilised":[143],"to":[144,174,191],"feedback":[151,163],"controller":[152],"discussed.":[154],"Criteria":[155],"cycle-stabilisation":[158],"established.":[160],"All":[161],"controllers":[164],"which":[165],"implement":[166],"minimal":[168],"length":[169],"from":[171],"each":[172],"obtained":[179],"using":[181],"proposed":[183],"algorithm.":[184],"Finally,":[185],"illustrative":[187],"example":[188],"presented":[190],"show":[192],"theoretical":[194],"results.":[195]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":7},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":1}],"updated_date":"2026-05-02T08:42:23.175194","created_date":"2025-10-10T00:00:00"}
