{"id":"https://openalex.org/W1990746578","doi":"https://doi.org/10.1109/tac.2012.2229840","title":"Sufficient and Necessary LMI Conditions for Robust Stability of Rationally Time-Varying Uncertain Systems","display_name":"Sufficient and Necessary LMI Conditions for Robust Stability of Rationally Time-Varying Uncertain Systems","publication_year":2012,"publication_date":"2012-11-22","ids":{"openalex":"https://openalex.org/W1990746578","doi":"https://doi.org/10.1109/tac.2012.2229840","mag":"1990746578"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2012.2229840","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2012.2229840","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/A5054609231","display_name":"Graziano Chesi","orcid":"https://orcid.org/0000-0003-4214-4224"},"institutions":[{"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":["HK"],"is_corresponding":true,"raw_author_name":"Graziano Chesi","raw_affiliation_strings":["Department of Electrical and Electronic Engineering, University of Hong Kong","Department of Electrical and Electronic Engineering,University of Hong Kong"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Electronic Engineering, University of Hong Kong","institution_ids":["https://openalex.org/I889458895"]},{"raw_affiliation_string":"Department of Electrical and Electronic Engineering,University of Hong Kong","institution_ids":["https://openalex.org/I889458895"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5054609231"],"corresponding_institution_ids":["https://openalex.org/I889458895"],"apc_list":null,"apc_paid":null,"fwci":3.3781,"has_fulltext":false,"cited_by_count":25,"citation_normalized_percentile":{"value":0.92050662,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"58","issue":"6","first_page":"1546","last_page":"1551"},"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":0.9998999834060669,"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":0.9998999834060669,"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/T11236","display_name":"Control Systems and Identification","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/T10876","display_name":"Fault Detection and Control Systems","score":0.9983000159263611,"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/polytope","display_name":"Polytope","score":0.787635087966919},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.723199725151062},{"id":"https://openalex.org/keywords/linear-matrix-inequality","display_name":"Linear matrix inequality","score":0.6586587429046631},{"id":"https://openalex.org/keywords/explained-sum-of-squares","display_name":"Explained sum of squares","score":0.608780562877655},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.5801253318786621},{"id":"https://openalex.org/keywords/simplex","display_name":"Simplex","score":0.5739606022834778},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.5157099366188049},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4601472318172455},{"id":"https://openalex.org/keywords/robust-control","display_name":"Robust control","score":0.454393208026886},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.44724196195602417},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4239218831062317},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.404674232006073},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.337602436542511},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.19613948464393616},{"id":"https://openalex.org/keywords/control-system","display_name":"Control system","score":0.17477628588676453},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.1739867627620697},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.16887113451957703},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.12080222368240356},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.10077130794525146},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.08199471235275269}],"concepts":[{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.787635087966919},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.723199725151062},{"id":"https://openalex.org/C201829737","wikidata":"https://www.wikidata.org/wiki/Q2022760","display_name":"Linear matrix inequality","level":2,"score":0.6586587429046631},{"id":"https://openalex.org/C49847556","wikidata":"https://www.wikidata.org/wiki/Q3964631","display_name":"Explained sum of squares","level":2,"score":0.608780562877655},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.5801253318786621},{"id":"https://openalex.org/C62438384","wikidata":"https://www.wikidata.org/wiki/Q331350","display_name":"Simplex","level":2,"score":0.5739606022834778},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.5157099366188049},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4601472318172455},{"id":"https://openalex.org/C31531917","wikidata":"https://www.wikidata.org/wiki/Q915157","display_name":"Robust control","level":3,"score":0.454393208026886},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.44724196195602417},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4239218831062317},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.404674232006073},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.337602436542511},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.19613948464393616},{"id":"https://openalex.org/C17500928","wikidata":"https://www.wikidata.org/wiki/Q959968","display_name":"Control system","level":2,"score":0.17477628588676453},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.1739867627620697},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.16887113451957703},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.12080222368240356},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.10077130794525146},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.08199471235275269},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"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/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"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/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","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/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tac.2012.2229840","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2012.2229840","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:hub.hku.hk:10722/184513","is_oa":false,"landing_page_url":"http://hdl.handle.net/10722/184513","pdf_url":null,"source":{"id":"https://openalex.org/S4377196271","display_name":"The HKU Scholars Hub (University of Hong Kong)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I889458895","host_organization_name":"University of Hong Kong","host_organization_lineage":["https://openalex.org/I889458895"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.4099999964237213,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W131296717","https://openalex.org/W1575783483","https://openalex.org/W1591868040","https://openalex.org/W1600295805","https://openalex.org/W1880805667","https://openalex.org/W1978587117","https://openalex.org/W1996715315","https://openalex.org/W1998204024","https://openalex.org/W2019016008","https://openalex.org/W2068617307","https://openalex.org/W2094973444","https://openalex.org/W2103594601","https://openalex.org/W2120198279","https://openalex.org/W2120207446","https://openalex.org/W2129492921","https://openalex.org/W2142759942","https://openalex.org/W2147439098","https://openalex.org/W2152327179","https://openalex.org/W2155724501","https://openalex.org/W2157269960","https://openalex.org/W2160391281","https://openalex.org/W2178412471","https://openalex.org/W2180693152","https://openalex.org/W3210839039"],"related_works":["https://openalex.org/W1642182499","https://openalex.org/W4286870264","https://openalex.org/W2279275934","https://openalex.org/W4304687059","https://openalex.org/W4242784854","https://openalex.org/W2963235221","https://openalex.org/W2291706033","https://openalex.org/W2131905798","https://openalex.org/W2163959792","https://openalex.org/W2131901345"],"abstract_inverted_index":{"This":[0],"technical":[1,22,60,83],"note":[2,23,61,84],"addresses":[3],"robust":[4],"stability":[5],"of":[6,48,52,73],"uncertain":[7],"systems":[8],"with":[9],"rational":[10],"dependence":[11],"on":[12,38,45,93],"unknown":[13],"time-varying":[14],"parameters":[15],"constrained":[16],"in":[17,117],"a":[18,26,63],"polytope.":[19],"First,":[20],"the":[21,46,59,74,82,94,118],"proves":[24],"that":[25,33,103],"sufficient":[27,65,104],"linear":[28,95],"matrix":[29],"inequality":[30],"(LMI)":[31],"condition":[32,69],"we":[34],"previously":[35],"proposed,":[36],"based":[37,92],"homogeneous":[39],"polynomial":[40],"Lyapunov":[41],"functions":[42],"(HPLFs)":[43],"and":[44,66,76,90,105],"introduction":[47],"an":[49],"extended":[50],"version":[51],"Polya's":[53],"theorem,":[54],"is":[55,100],"also":[56],"necessary.":[57],"Second,":[58],"proposes":[62],"new":[64],"necessary":[67,106],"LMI":[68,107],"by":[70],"exploiting":[71],"properties":[72],"simplex":[75],"sum-of-squares":[77],"(SOS)":[78],"parameter-dependent":[79],"polynomials.":[80],"Lastly,":[81],"investigates":[85],"relationships":[86],"among":[87],"these":[88],"conditions":[89,91,108],"fractional":[96],"representation":[97],"(LFR).":[98],"It":[99],"worth":[101],"remarking":[102],"for":[109],"this":[110],"problem":[111],"have":[112],"not":[113],"been":[114],"proposed":[115],"yet":[116],"literature.":[119]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
