{"id":"https://openalex.org/W2155267437","doi":"https://doi.org/10.1109/tac.2010.2050162","title":"Stability Crossing Set for Systems With Three Delays","display_name":"Stability Crossing Set for Systems With Three Delays","publication_year":2010,"publication_date":"2010-05-26","ids":{"openalex":"https://openalex.org/W2155267437","doi":"https://doi.org/10.1109/tac.2010.2050162","mag":"2155267437"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2010.2050162","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2010.2050162","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/A5086584348","display_name":"Keqin Gu","orcid":"https://orcid.org/0000-0003-2587-4284"},"institutions":[{"id":"https://openalex.org/I87547150","display_name":"Southern Illinois University Edwardsville","ror":"https://ror.org/04cqs5j56","country_code":"US","type":"education","lineage":["https://openalex.org/I2801502357","https://openalex.org/I87547150"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Keqin Gu","raw_affiliation_strings":["Department of Mechanical and Industrial Engineering, Southern Illinois University Edwardsville, Edwardsville, IL, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mechanical and Industrial Engineering, Southern Illinois University Edwardsville, Edwardsville, IL, USA","institution_ids":["https://openalex.org/I87547150"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5068594775","display_name":"Mohammad Naghnaeian","orcid":"https://orcid.org/0000-0002-2136-4239"},"institutions":[{"id":"https://openalex.org/I87547150","display_name":"Southern Illinois University Edwardsville","ror":"https://ror.org/04cqs5j56","country_code":"US","type":"education","lineage":["https://openalex.org/I2801502357","https://openalex.org/I87547150"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Mohammad Naghnaeian","raw_affiliation_strings":["Department of Mechanical and Industrial Engineering, Southern Illinois University Edwardsville, Edwardsville, IL, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mechanical and Industrial Engineering, Southern Illinois University Edwardsville, Edwardsville, IL, USA","institution_ids":["https://openalex.org/I87547150"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5086584348"],"corresponding_institution_ids":["https://openalex.org/I87547150"],"apc_list":null,"apc_paid":null,"fwci":5.7808,"has_fulltext":false,"cited_by_count":61,"citation_normalized_percentile":{"value":0.95863012,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"56","issue":"1","first_page":"11","last_page":"26"},"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":0.9968000054359436,"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":0.9968000054359436,"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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.995199978351593,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T10244","display_name":"Chaos control and synchronization","score":0.9894000291824341,"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/grashof-number","display_name":"Grashof number","score":0.6828980445861816},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6263953447341919},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5401638150215149},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.5394080877304077},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.49839305877685547},{"id":"https://openalex.org/keywords/degenerate-energy-levels","display_name":"Degenerate energy levels","score":0.4514755308628082},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.4257115423679352},{"id":"https://openalex.org/keywords/level-crossing","display_name":"Level crossing","score":0.41450974345207214},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.3493890166282654},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3376423418521881},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.28408658504486084},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.21530014276504517},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.13934680819511414},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10042339563369751}],"concepts":[{"id":"https://openalex.org/C13027520","wikidata":"https://www.wikidata.org/wiki/Q868719","display_name":"Grashof number","level":5,"score":0.6828980445861816},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6263953447341919},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5401638150215149},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.5394080877304077},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.49839305877685547},{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.4514755308628082},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.4257115423679352},{"id":"https://openalex.org/C1975866","wikidata":"https://www.wikidata.org/wiki/Q171448","display_name":"Level crossing","level":2,"score":0.41450974345207214},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3493890166282654},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3376423418521881},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.28408658504486084},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.21530014276504517},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.13934680819511414},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10042339563369751},{"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/C95457728","wikidata":"https://www.wikidata.org/wiki/Q309","display_name":"History","level":0,"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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C130230704","wikidata":"https://www.wikidata.org/wiki/Q898280","display_name":"Nusselt number","level":4,"score":0.0},{"id":"https://openalex.org/C182748727","wikidata":"https://www.wikidata.org/wiki/Q178932","display_name":"Reynolds number","level":3,"score":0.0},{"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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C196558001","wikidata":"https://www.wikidata.org/wiki/Q190132","display_name":"Turbulence","level":2,"score":0.0},{"id":"https://openalex.org/C166957645","wikidata":"https://www.wikidata.org/wiki/Q23498","display_name":"Archaeology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tac.2010.2050162","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2010.2050162","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":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W590413840","https://openalex.org/W658670873","https://openalex.org/W1487864787","https://openalex.org/W1502089761","https://openalex.org/W1506119886","https://openalex.org/W1607633954","https://openalex.org/W1965431946","https://openalex.org/W1969266494","https://openalex.org/W1975915100","https://openalex.org/W1981483679","https://openalex.org/W1992572795","https://openalex.org/W1996874155","https://openalex.org/W1999846863","https://openalex.org/W2001821873","https://openalex.org/W2014172170","https://openalex.org/W2035841808","https://openalex.org/W2048935624","https://openalex.org/W2062210472","https://openalex.org/W2074178424","https://openalex.org/W2079305541","https://openalex.org/W2086295052","https://openalex.org/W2089876099","https://openalex.org/W2100757047","https://openalex.org/W2144974199","https://openalex.org/W2157023863","https://openalex.org/W2179522436","https://openalex.org/W2467963231","https://openalex.org/W2522123876","https://openalex.org/W2525143841","https://openalex.org/W2625711953","https://openalex.org/W4211202937","https://openalex.org/W4231563473","https://openalex.org/W4239355989","https://openalex.org/W4285719527","https://openalex.org/W4293087381","https://openalex.org/W6726521486","https://openalex.org/W6739083902"],"related_works":["https://openalex.org/W2728224919","https://openalex.org/W2951521427","https://openalex.org/W2476351798","https://openalex.org/W2783654391","https://openalex.org/W2031004667","https://openalex.org/W2970673251","https://openalex.org/W2963905608","https://openalex.org/W2319454029","https://openalex.org/W3107737229","https://openalex.org/W2024154456"],"abstract_inverted_index":{"This":[0],"article":[1,82],"describes":[2],"the":[3,32,37,55,59,67,71,76,95,106,111],"stability":[4,60,96],"crossing":[5,18,61,72,97,112],"set":[6,62,98],"for":[7],"linear":[8,100],"time-delay":[9],"systems":[10,101,128],"of":[11,23,29,31,48,58,70,78,86,94,99,109,119,123],"arbitrary":[12],"order":[13],"with":[14,102,129],"three":[15,103],"delays.":[16,104],"The":[17],"frequency":[19,73],"set,":[20],"which":[21],"consists":[22],"all":[24],"frequencies":[25],"where":[26],"a":[27,84,116],"pair":[28],"zeros":[30],"characteristic":[33],"quasipolynomial":[34],"may":[35],"cross":[36],"imaginary":[38],"axis,":[39],"is":[40,63,133],"partitioned":[41],"to":[42,127],"Grashof":[43],"sets":[44,47],"and":[45,88,91],"Non-Grashof":[46],"various":[49],"types.":[50],"It":[51],"was":[52],"found":[53],"that":[54],"general":[56],"characteristics":[57],"completely":[64],"determined":[65],"by":[66],"partition":[68],"structure":[69],"set.":[74],"With":[75,105],"exception":[77],"degenerate":[79],"cases,":[80],"this":[81,114],"provides":[83,115],"method":[85,108,118],"explicit":[87],"complete":[89],"parameterization":[90],"geometric":[92],"characterization":[93],"well-known":[107],"finding":[110,120],"directions,":[113],"powerful":[117],"parameter":[121],"regions":[122],"stable":[124],"systems.":[125],"Extension":[126],"additional":[130],"fixed":[131],"delays":[132],"also":[134],"discussed.":[135]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":9},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
