{"id":"https://openalex.org/W4375929274","doi":"https://doi.org/10.1109/tac.2023.3274208","title":"External Direct Sum Invariant Subspace and Decomposition of Coupled Differential-Difference Equations","display_name":"External Direct Sum Invariant Subspace and Decomposition of Coupled Differential-Difference Equations","publication_year":2023,"publication_date":"2023-05-08","ids":{"openalex":"https://openalex.org/W4375929274","doi":"https://doi.org/10.1109/tac.2023.3274208"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2023.3274208","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2023.3274208","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 Mechatronics Engineering, Southern Illinois University Edwardsville, Edwardsville, IL, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mechanical and Mechatronics Engineering, Southern Illinois University Edwardsville, Edwardsville, IL, USA","institution_ids":["https://openalex.org/I87547150"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5092340566","display_name":"Huan Phan\u2010Van","orcid":"https://orcid.org/0009-0001-4741-5284"},"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":"Huan Phan-Van","raw_affiliation_strings":["Department of Mechanical and Mechatronics Engineering, Southern Illinois University Edwardsville, Edwardsville, IL, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mechanical and Mechatronics 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":1.6457,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.79954899,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"69","issue":"2","first_page":"1022","last_page":"1028"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9987000226974487,"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":0.9987000226974487,"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9939000010490417,"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"}},{"id":"https://openalex.org/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.9912999868392944,"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":0.7520366907119751},{"id":"https://openalex.org/keywords/linear-subspace","display_name":"Linear subspace","score":0.7095280885696411},{"id":"https://openalex.org/keywords/invariant-subspace","display_name":"Invariant subspace","score":0.626520574092865},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.6205928921699524},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.6170018911361694},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.48488980531692505},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.472744345664978},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.46394893527030945},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4326220750808716},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3136272728443146},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.1603160798549652},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0795941948890686},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.06863698363304138}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7520366907119751},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.7095280885696411},{"id":"https://openalex.org/C2777059694","wikidata":"https://www.wikidata.org/wiki/Q2706744","display_name":"Invariant subspace","level":3,"score":0.626520574092865},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.6205928921699524},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.6170018911361694},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.48488980531692505},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.472744345664978},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.46394893527030945},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4326220750808716},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3136272728443146},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.1603160798549652},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0795941948890686},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.06863698363304138},{"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tac.2023.3274208","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2023.3274208","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"},{"id":"pmh:oai:spark.siue.edu:siue_fac-1179","is_oa":false,"landing_page_url":"https://spark.siue.edu/siue_fac/160","pdf_url":null,"source":{"id":"https://openalex.org/S4377196622","display_name":"SPARK (Southern Illinois University Edwardsville)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I87547150","host_organization_name":"Southern Illinois University Edwardsville","host_organization_lineage":["https://openalex.org/I87547150"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIUE Faculty Research, Scholarship, and Creative Activity","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W188866077","https://openalex.org/W1965593229","https://openalex.org/W1995007479","https://openalex.org/W2002045670","https://openalex.org/W2039137535","https://openalex.org/W2097280120","https://openalex.org/W2125457292","https://openalex.org/W3125820033","https://openalex.org/W4211202937","https://openalex.org/W4231563473","https://openalex.org/W4254742956","https://openalex.org/W4294692005"],"related_works":["https://openalex.org/W4235906205","https://openalex.org/W4301478900","https://openalex.org/W102084567","https://openalex.org/W2118409924","https://openalex.org/W2948021207","https://openalex.org/W4221145148","https://openalex.org/W2978618494","https://openalex.org/W4285219056","https://openalex.org/W1964071455","https://openalex.org/W67811872"],"abstract_inverted_index":{"This":[0,25],"article":[1],"discusses":[2],"the":[3,30,38,42,54,63,87],"invariant":[4,23],"subspaces":[5],"that":[6,19],"are":[7,17,89],"restricted":[8],"to":[9,29,37],"be":[10],"external":[11],"direct":[12],"sums.":[13],"Some":[14],"existence":[15],"conditions":[16],"presented":[18],"facilitate":[20],"finding":[21],"such":[22],"subspaces.":[24],"problem":[26],"is":[27,76],"related":[28],"decomposition":[31],"of":[32,40,44,56,85,92],"coupled":[33,45,57],"differential-difference":[34,46,58],"equations,":[35],"leading":[36],"possibility":[39],"lowering":[41,53],"dimensions":[43],"equations.":[47],"As":[48],"has":[49],"been":[50],"well":[51],"documented,":[52],"dimension":[55],"equations":[59],"can":[60],"drastically":[61],"reduce":[62],"computational":[64],"time":[65],"needed":[66],"in":[67],"stability":[68],"analysis":[69],"when":[70],"a":[71],"complete":[72],"quadratic":[73],"Lyapunov\u2013Krasovskii":[74],"functional":[75],"used.":[77],"Most":[78],"known":[79],"<italic":[80],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[81],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">ad":[82],"hoc</i>":[83],"methods":[84],"reducing":[86],"order":[88],"special":[90],"cases":[91],"this":[93],"formulation.":[94]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
