{"id":"https://openalex.org/W3211063834","doi":"https://doi.org/10.1109/tac.2021.3122380","title":"Positivity and Stability Analysis of Homogeneous Coupled Differential-Difference Equations With Time-Varying Delays","display_name":"Positivity and Stability Analysis of Homogeneous Coupled Differential-Difference Equations With Time-Varying Delays","publication_year":2021,"publication_date":"2021-10-26","ids":{"openalex":"https://openalex.org/W3211063834","doi":"https://doi.org/10.1109/tac.2021.3122380","mag":"3211063834"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2021.3122380","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2021.3122380","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5048253771","display_name":"Yukang Cui","orcid":"https://orcid.org/0000-0001-8783-7441"},"institutions":[{"id":"https://openalex.org/I4210136793","display_name":"Peng Cheng Laboratory","ror":"https://ror.org/03qdqbt06","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210136793"]},{"id":"https://openalex.org/I180726961","display_name":"Shenzhen University","ror":"https://ror.org/01vy4gh70","country_code":"CN","type":"education","lineage":["https://openalex.org/I180726961"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yukang Cui","raw_affiliation_strings":["Guangdong Key Laboratory of Electromagnetic Control and Intelligent Robots, The College of Mechatronics and Control Engineering, Shenzhen University, Shenzhen, China","Peng Cheng Laboratory, Shenzhen, China"],"affiliations":[{"raw_affiliation_string":"Guangdong Key Laboratory of Electromagnetic Control and Intelligent Robots, The College of Mechatronics and Control Engineering, Shenzhen University, Shenzhen, China","institution_ids":["https://openalex.org/I180726961"]},{"raw_affiliation_string":"Peng Cheng Laboratory, Shenzhen, China","institution_ids":["https://openalex.org/I4210136793"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5017887363","display_name":"Jun Shen","orcid":"https://orcid.org/0000-0002-0361-0512"},"institutions":[{"id":"https://openalex.org/I9842412","display_name":"Nanjing University of Aeronautics and Astronautics","ror":"https://ror.org/01scyh794","country_code":"CN","type":"education","lineage":["https://openalex.org/I9842412"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jun Shen","raw_affiliation_strings":["College of Automation Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, China"],"affiliations":[{"raw_affiliation_string":"College of Automation Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, China","institution_ids":["https://openalex.org/I9842412"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100441598","display_name":"Wei Zhang","orcid":"https://orcid.org/0000-0002-3000-6038"},"institutions":[{"id":"https://openalex.org/I50180762","display_name":"Chongqing Three Gorges University","ror":"https://ror.org/05rs3pv16","country_code":"CN","type":"education","lineage":["https://openalex.org/I50180762"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wei Zhang","raw_affiliation_strings":["School of Three Gorges Artificial Intelligence, Chongqing Three Gorges University, Chongqing, China"],"affiliations":[{"raw_affiliation_string":"School of Three Gorges Artificial Intelligence, Chongqing Three Gorges University, Chongqing, China","institution_ids":["https://openalex.org/I50180762"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5044290768","display_name":"Zhiguang Feng","orcid":"https://orcid.org/0000-0003-1037-1529"},"institutions":[{"id":"https://openalex.org/I151727225","display_name":"Harbin Engineering University","ror":"https://ror.org/03x80pn82","country_code":"CN","type":"education","lineage":["https://openalex.org/I151727225"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhiguang Feng","raw_affiliation_strings":["College of Automation, Harbin Engineering University, Harbin, China"],"affiliations":[{"raw_affiliation_string":"College of Automation, Harbin Engineering University, Harbin, China","institution_ids":["https://openalex.org/I151727225"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5088135162","display_name":"Xin Gong","orcid":"https://orcid.org/0000-0001-6883-5088"},"institutions":[{"id":"https://openalex.org/I180726961","display_name":"Shenzhen University","ror":"https://ror.org/01vy4gh70","country_code":"CN","type":"education","lineage":["https://openalex.org/I180726961"]},{"id":"https://openalex.org/I889458895","display_name":"University of Hong Kong","ror":"https://ror.org/02zhqgq86","country_code":"HK","type":"education","lineage":["https://openalex.org/I889458895"]}],"countries":["CN","HK"],"is_corresponding":false,"raw_author_name":"Xin Gong","raw_affiliation_strings":["College of Mechatronics and Control Engineering, Shenzhen University, Shenzhen, China","Department of Mechanical Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong"],"affiliations":[{"raw_affiliation_string":"College of Mechatronics and Control Engineering, Shenzhen University, Shenzhen, China","institution_ids":["https://openalex.org/I180726961"]},{"raw_affiliation_string":"Department of Mechanical Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong","institution_ids":["https://openalex.org/I889458895"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5048253771"],"corresponding_institution_ids":["https://openalex.org/I180726961","https://openalex.org/I4210136793"],"apc_list":null,"apc_paid":null,"fwci":5.2229,"has_fulltext":false,"cited_by_count":23,"citation_normalized_percentile":{"value":0.96286107,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"67","issue":"10","first_page":"5493","last_page":"5500"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9979000091552734,"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"}},"topics":[{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9979000091552734,"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/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9957000017166138,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9945999979972839,"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/mathematics","display_name":"Mathematics","score":0.7887516617774963},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.6625327467918396},{"id":"https://openalex.org/keywords/homogeneous","display_name":"Homogeneous","score":0.6470229625701904},{"id":"https://openalex.org/keywords/homogeneity","display_name":"Homogeneity (statistics)","score":0.6071692109107971},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5147294998168945},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5041736364364624},{"id":"https://openalex.org/keywords/homogeneous-differential-equation","display_name":"Homogeneous differential equation","score":0.49180176854133606},{"id":"https://openalex.org/keywords/exponential-stability","display_name":"Exponential stability","score":0.47634103894233704},{"id":"https://openalex.org/keywords/bounding-overwatch","display_name":"Bounding overwatch","score":0.4606037735939026},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.45743611454963684},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.44222432374954224},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.39358463883399963},{"id":"https://openalex.org/keywords/differential-algebraic-equation","display_name":"Differential algebraic equation","score":0.1815902292728424},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.15210282802581787},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12373396754264832},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.0916113555431366},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.08200094103813171}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7887516617774963},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.6625327467918396},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.6470229625701904},{"id":"https://openalex.org/C142259097","wikidata":"https://www.wikidata.org/wiki/Q5891314","display_name":"Homogeneity (statistics)","level":2,"score":0.6071692109107971},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5147294998168945},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5041736364364624},{"id":"https://openalex.org/C22219631","wikidata":"https://www.wikidata.org/wiki/Q2434565","display_name":"Homogeneous differential equation","level":5,"score":0.49180176854133606},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.47634103894233704},{"id":"https://openalex.org/C63584917","wikidata":"https://www.wikidata.org/wiki/Q333286","display_name":"Bounding overwatch","level":2,"score":0.4606037735939026},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.45743611454963684},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.44222432374954224},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.39358463883399963},{"id":"https://openalex.org/C186219872","wikidata":"https://www.wikidata.org/wiki/Q955889","display_name":"Differential algebraic equation","level":4,"score":0.1815902292728424},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.15210282802581787},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12373396754264832},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0916113555431366},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.08200094103813171},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"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/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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tac.2021.3122380","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2021.3122380","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3753909859","display_name":null,"funder_award_id":"61603180","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4348437773","display_name":null,"funder_award_id":"61973156","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G709871273","display_name":null,"funder_award_id":"BK20200068","funder_id":"https://openalex.org/F4320322769","funder_display_name":"Natural Science Foundation of Jiangsu Province"},{"id":"https://openalex.org/G8927226219","display_name":null,"funder_award_id":"61903258","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322769","display_name":"Natural Science Foundation of Jiangsu Province","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W188485126","https://openalex.org/W1536762869","https://openalex.org/W1601754013","https://openalex.org/W1963748385","https://openalex.org/W1979188460","https://openalex.org/W1981737882","https://openalex.org/W1996116324","https://openalex.org/W2002045670","https://openalex.org/W2002241547","https://openalex.org/W2019691104","https://openalex.org/W2074283998","https://openalex.org/W2129681350","https://openalex.org/W2143294995","https://openalex.org/W2143927056","https://openalex.org/W2506307854","https://openalex.org/W2742255278","https://openalex.org/W2795039571","https://openalex.org/W2898296690","https://openalex.org/W2946965658","https://openalex.org/W2952730548","https://openalex.org/W2963734869","https://openalex.org/W3047593069","https://openalex.org/W4211137119","https://openalex.org/W4235143360","https://openalex.org/W4313372009"],"related_works":["https://openalex.org/W2041063044","https://openalex.org/W3120523813","https://openalex.org/W2028781854","https://openalex.org/W2370113799","https://openalex.org/W2892007971","https://openalex.org/W1969400912","https://openalex.org/W2058292572","https://openalex.org/W3179404742","https://openalex.org/W2896615262","https://openalex.org/W2031088914"],"abstract_inverted_index":{"This":[0],"article":[1],"studies":[2],"the":[3,23,43,48,63,71,82,91,104,107],"positivity":[4,18,34],"and":[5,39,46,65,90],"stability":[6,45,74],"of":[7,59,76,84,106],"homogeneous":[8,53,77],"coupled":[9,25,54,78],"differential-difference":[10,26,55,79],"equations":[11,27,56,80],"with":[12,28,57],"time-varying":[13],"delays.":[14,29],"First,":[15],"a":[16],"sufficient":[17,40,66],"condition":[19,67],"is":[20,68,86,94],"proposed":[21],"for":[22,51],"nonlinear":[24],"Then,":[30],"based":[31],"on":[32],"this":[33],"condition,":[35],"we":[36],"present":[37],"necessary":[38,64],"conditions":[41],"ensuring":[42],"exponential":[44],"bounding":[47],"decay":[49,92],"rate":[50,93],"time-delay":[52],"homogeneity":[58,85],"degree":[60,83],"one.":[61],"Furthermore,":[62],"extended":[69],"to":[70,102],"global":[72],"polynomial":[73],"analysis":[75],"when":[81],"greater":[87],"than":[88],"one,":[89],"also":[95],"investigated.":[96],"Two":[97],"numerical":[98],"examples":[99],"are":[100],"employed":[101],"show":[103],"effectiveness":[105],"obtained":[108],"results.":[109]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":9},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}