{"id":"https://openalex.org/W3003844222","doi":"https://doi.org/10.1080/00207721.2020.1716098","title":"A reliable graphical criterion for TDS stability analysis","display_name":"A reliable graphical criterion for TDS stability analysis","publication_year":2020,"publication_date":"2020-01-25","ids":{"openalex":"https://openalex.org/W3003844222","doi":"https://doi.org/10.1080/00207721.2020.1716098","mag":"3003844222"},"language":"en","primary_location":{"id":"doi:10.1080/00207721.2020.1716098","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207721.2020.1716098","pdf_url":null,"source":{"id":"https://openalex.org/S129640837","display_name":"International Journal of Systems Science","issn_l":"0020-7721","issn":["0020-7721","1464-5319"],"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 Systems Science","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/A5058566541","display_name":"Tiao Yang Cai","orcid":null},"institutions":[{"id":"https://openalex.org/I94611258","display_name":"Hebei Normal University","ror":"https://ror.org/004rbbw49","country_code":"CN","type":"education","lineage":["https://openalex.org/I94611258"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Tiao Yang Cai","raw_affiliation_strings":["College of Engineering, Hebei Normal University, Shijiazhuang, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"College of Engineering, Hebei Normal University, Shijiazhuang, People's Republic of China","institution_ids":["https://openalex.org/I94611258"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045502439","display_name":"Hui Jin","orcid":"https://orcid.org/0000-0002-1637-9946"},"institutions":[{"id":"https://openalex.org/I94611258","display_name":"Hebei Normal University","ror":"https://ror.org/004rbbw49","country_code":"CN","type":"education","lineage":["https://openalex.org/I94611258"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Hui Long Jin","raw_affiliation_strings":["College of Engineering, Hebei Normal University, Shijiazhuang, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"College of Engineering, Hebei Normal University, Shijiazhuang, People's Republic of China","institution_ids":["https://openalex.org/I94611258"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100746277","display_name":"Xiang Xie","orcid":"https://orcid.org/0000-0002-9282-2209"},"institutions":[{"id":"https://openalex.org/I41198531","display_name":"Nanjing University of Posts and Telecommunications","ror":"https://ror.org/043bpky34","country_code":"CN","type":"education","lineage":["https://openalex.org/I41198531"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiang Peng Xie","raw_affiliation_strings":["Institute of Advanced Technology, Nanjing University of Posts and Telecommunications, Nanjing, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"Institute of Advanced Technology, Nanjing University of Posts and Telecommunications, Nanjing, People's Republic of China","institution_ids":["https://openalex.org/I41198531"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5045502439"],"corresponding_institution_ids":["https://openalex.org/I94611258"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.01463644,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"51","issue":"2","first_page":"381","last_page":"388"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.9987000226974487,"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/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.9987000226974487,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9872000217437744,"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9846000075340271,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/stability","display_name":"Stability (learning theory)","score":0.7328193187713623},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6717671155929565},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.6163145303726196},{"id":"https://openalex.org/keywords/path","display_name":"Path (computing)","score":0.5677919387817383},{"id":"https://openalex.org/keywords/characteristic-equation","display_name":"Characteristic equation","score":0.5390230417251587},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5087900757789612},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.46958866715431213},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4625745117664337},{"id":"https://openalex.org/keywords/circle-criterion","display_name":"Circle criterion","score":0.45876023173332214},{"id":"https://openalex.org/keywords/stability-criterion","display_name":"Stability criterion","score":0.44987714290618896},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.44421273469924927},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4139164388179779},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.32406532764434814},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2702471613883972},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.25162652134895325},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.11864852905273438},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.10513761639595032},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.09814897179603577},{"id":"https://openalex.org/keywords/exponential-stability","display_name":"Exponential stability","score":0.08640587329864502},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.08527860045433044}],"concepts":[{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.7328193187713623},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6717671155929565},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.6163145303726196},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.5677919387817383},{"id":"https://openalex.org/C53744967","wikidata":"https://www.wikidata.org/wiki/Q1062971","display_name":"Characteristic equation","level":3,"score":0.5390230417251587},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5087900757789612},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.46958866715431213},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4625745117664337},{"id":"https://openalex.org/C65521940","wikidata":"https://www.wikidata.org/wiki/Q5121443","display_name":"Circle criterion","level":4,"score":0.45876023173332214},{"id":"https://openalex.org/C2778925954","wikidata":"https://www.wikidata.org/wiki/Q16883749","display_name":"Stability criterion","level":3,"score":0.44987714290618896},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.44421273469924927},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4139164388179779},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.32406532764434814},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2702471613883972},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.25162652134895325},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.11864852905273438},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.10513761639595032},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.09814897179603577},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.08640587329864502},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.08527860045433044},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","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},{"id":"https://openalex.org/C55689738","wikidata":"https://www.wikidata.org/wiki/Q15963867","display_name":"Discrete time and continuous time","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1080/00207721.2020.1716098","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207721.2020.1716098","pdf_url":null,"source":{"id":"https://openalex.org/S129640837","display_name":"International Journal of Systems Science","issn_l":"0020-7721","issn":["0020-7721","1464-5319"],"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 Systems Science","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:taf:tsysxx:v:51:y:2020:i:2:p:381-388","is_oa":false,"landing_page_url":"http://hdl.handle.net/10.1080/00207721.2020.1716098","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W1491331964","https://openalex.org/W1965431946","https://openalex.org/W1973695175","https://openalex.org/W1975879384","https://openalex.org/W1989107982","https://openalex.org/W1989251100","https://openalex.org/W2007456116","https://openalex.org/W2010006653","https://openalex.org/W2014172170","https://openalex.org/W2022419653","https://openalex.org/W2027876948","https://openalex.org/W2029185800","https://openalex.org/W2033289452","https://openalex.org/W2074178424","https://openalex.org/W2080529473","https://openalex.org/W2100757047","https://openalex.org/W2104501242","https://openalex.org/W2118687002","https://openalex.org/W2145615018","https://openalex.org/W2149971042","https://openalex.org/W2160854968","https://openalex.org/W2182851541","https://openalex.org/W2795341752","https://openalex.org/W2903320160","https://openalex.org/W2913909435","https://openalex.org/W2915803738","https://openalex.org/W4231563473","https://openalex.org/W4246432872","https://openalex.org/W4285719527","https://openalex.org/W4293087381"],"related_works":["https://openalex.org/W2130216035","https://openalex.org/W2043892938","https://openalex.org/W1970104640","https://openalex.org/W2040080498","https://openalex.org/W166939899","https://openalex.org/W2093530324","https://openalex.org/W1976068816","https://openalex.org/W2329833644","https://openalex.org/W2117288475","https://openalex.org/W2517947555"],"abstract_inverted_index":{"The":[0],"paper":[1],"considers":[2],"the":[3,19,32,53,70,83,103],"stability":[4,49],"issue":[5,13],"of":[6,21,23,31,55,72,86],"linear":[7],"systems":[8],"with":[9,61],"commensurate":[10],"delays.":[11],"This":[12],"can":[14],"be":[15],"well":[16],"characterised":[17],"by":[18],"distribution":[20,29],"roots":[22,33,57],"system's":[24],"characteristic":[25,87],"equation.":[26],"At":[27,94],"first,":[28],"boundary":[30],"(with":[34],"positive":[35],"real":[36],"parts)":[37],"is":[38,58,92,107],"explicit":[39],"given":[40,99],"in":[41,69,89],"a":[42,46,79],"practical":[43],"way.":[44],"Subsequently,":[45],"reliable":[47,108],"graphical":[48],"criterion":[50],"for":[51,81],"calculating":[52],"number":[54],"unstable":[56],"deduced,":[59],"associating":[60],"auxiliary":[62],"polynomial":[63],"which":[64],"plays":[65],"an":[66],"important":[67],"role":[68],"analysis":[71],"high":[73],"order":[74],"and":[75,109],"complex":[76],"systems.":[77],"Moreover,":[78],"procedure":[80],"drawing":[82],"winding":[84],"curve":[85],"function":[88],"finite":[90],"path":[91],"proposed.":[93],"last,":[95],"typical":[96],"examples":[97],"are":[98],"to":[100],"illustrate":[101],"that":[102],"result":[104],"carried":[105],"out":[106],"efficient.":[110]},"counts_by_year":[{"year":2024,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
