{"id":"https://openalex.org/W2093830732","doi":"https://doi.org/10.1137/s0895479801389710","title":"Solvability Conditions and Parameterization of All Solutions for the Triangular Decoupling Problem","display_name":"Solvability Conditions and Parameterization of All Solutions for the Triangular Decoupling Problem","publication_year":2002,"publication_date":"2002-01-01","ids":{"openalex":"https://openalex.org/W2093830732","doi":"https://doi.org/10.1137/s0895479801389710","mag":"2093830732"},"language":"en","primary_location":{"id":"doi:10.1137/s0895479801389710","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479801389710","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Matrix Analysis and Applications","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/A5102966756","display_name":"Delin Chu","orcid":"https://orcid.org/0000-0001-7736-7490"},"institutions":[{"id":"https://openalex.org/I165932596","display_name":"National University of Singapore","ror":"https://ror.org/01tgyzw49","country_code":"SG","type":"education","lineage":["https://openalex.org/I165932596"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Delin Chu","raw_affiliation_strings":["National University of Singapore"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"National University of Singapore","institution_ids":["https://openalex.org/I165932596"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5109412865","display_name":"Roger C. E. Tan","orcid":"https://orcid.org/0009-0009-3531-2294"},"institutions":[{"id":"https://openalex.org/I165932596","display_name":"National University of Singapore","ror":"https://ror.org/01tgyzw49","country_code":"SG","type":"education","lineage":["https://openalex.org/I165932596"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Roger C. E. Tan","raw_affiliation_strings":["National University of Singapore"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"National University of Singapore","institution_ids":["https://openalex.org/I165932596"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I165932596"],"apc_list":null,"apc_paid":null,"fwci":1.2731,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.80360437,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"23","issue":"4","first_page":"1171","last_page":"1182"},"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":0.9975000023841858,"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":0.9975000023841858,"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/T11749","display_name":"Iterative Learning Control Systems","score":0.9937999844551086,"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/T10571","display_name":"Robotic Mechanisms and Dynamics","score":0.9907000064849854,"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/decoupling","display_name":"Decoupling (probability)","score":0.8981151580810547},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8746308088302612},{"id":"https://openalex.org/keywords/parameterized-complexity","display_name":"Parameterized complexity","score":0.7814273834228516},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.48429933190345764},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.45849621295928955},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.43436217308044434},{"id":"https://openalex.org/keywords/triangular-matrix","display_name":"Triangular matrix","score":0.4138113856315613},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2965237498283386},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.28896474838256836},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.06068316102027893}],"concepts":[{"id":"https://openalex.org/C205606062","wikidata":"https://www.wikidata.org/wiki/Q5249645","display_name":"Decoupling (probability)","level":2,"score":0.8981151580810547},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8746308088302612},{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.7814273834228516},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.48429933190345764},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.45849621295928955},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.43436217308044434},{"id":"https://openalex.org/C104528550","wikidata":"https://www.wikidata.org/wiki/Q506265","display_name":"Triangular matrix","level":3,"score":0.4138113856315613},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2965237498283386},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.28896474838256836},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.06068316102027893},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C133731056","wikidata":"https://www.wikidata.org/wiki/Q4917288","display_name":"Control engineering","level":1,"score":0.0},{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s0895479801389710","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479801389710","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Matrix Analysis and Applications","raw_type":"journal-article"},{"id":"pmh:oai:scholarbank.nus.edu.sg:10635/104144","is_oa":false,"landing_page_url":"http://scholarbank.nus.edu.sg/handle/10635/104144","pdf_url":null,"source":{"id":"https://openalex.org/S7407052290","display_name":"National University of Singapore","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Scopus","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":8,"referenced_works":["https://openalex.org/W1984609509","https://openalex.org/W1996322939","https://openalex.org/W2002897949","https://openalex.org/W2011373218","https://openalex.org/W2018607720","https://openalex.org/W2057244606","https://openalex.org/W2065203034","https://openalex.org/W2084275220"],"related_works":["https://openalex.org/W2051058708","https://openalex.org/W154868527","https://openalex.org/W1494268238","https://openalex.org/W1983207144","https://openalex.org/W2490706771","https://openalex.org/W2480116122","https://openalex.org/W4255576661","https://openalex.org/W2023329664","https://openalex.org/W1967452912","https://openalex.org/W4308012852"],"abstract_inverted_index":{"This":[0],"is":[1,77,82],"the":[2,26,70],"sequel":[3],"to":[4],"[D.":[5],"Chu":[6],"and":[7,37,62,96],"R.":[8],"C.":[9],"E.":[10],"Tan,":[11],"SIAM":[12],"J.":[13],"Matrix":[14],"nal.":[15],"Appl.,":[16],"23":[17],"(2002),":[18],"pp.":[19],"1143-1170].":[20],"In":[21,46],"that":[22],"paper":[23,48],"we":[24,49],"studied":[25],"row":[27,29],"by":[28],"decoupling":[30,55],"problem":[31],"with":[32],"stability":[33],"in":[34,102],"control":[35],"theory":[36],"developed":[38],"a":[39,51,78,103],"numerically":[40,104],"reliable":[41],"method":[42],"for":[43],"solving":[44],"it.":[45],"this":[47],"study":[50],"related":[52],"problem---the":[53],"triangular":[54],"problem.":[56],"We":[57],"not":[58],"only":[59,85],"give":[60],"new":[61,90],"explicit":[63],"solvability":[64,91],"conditions":[65,92],"but":[66],"also":[67],"parameterize":[68],"all":[69,97],"solutions.":[71],"The":[72],"basis":[73],"of":[74],"our":[75,89],"result":[76],"condensed":[79],"form":[80],"which":[81],"computed":[83],"using":[84],"orthogonal":[86],"transformations.":[87],"Hence,":[88],"can":[93,99],"be":[94,100],"verified":[95],"solutions":[98],"parameterized":[101],"stable":[105],"manner.":[106]},"counts_by_year":[{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}