{"id":"https://openalex.org/W3170501521","doi":"https://doi.org/10.1109/tac.2021.3088810","title":"Analysis of Positive Systems With Input Saturation: Invariant Hyperpyramids and Hyperrectangles","display_name":"Analysis of Positive Systems With Input Saturation: Invariant Hyperpyramids and Hyperrectangles","publication_year":2021,"publication_date":"2021-06-14","ids":{"openalex":"https://openalex.org/W3170501521","doi":"https://doi.org/10.1109/tac.2021.3088810","mag":"3170501521"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2021.3088810","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2021.3088810","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/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":true,"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":"last","author":{"id":"https://openalex.org/A5038930344","display_name":"James Lam","orcid":"https://orcid.org/0000-0002-0294-0640"},"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":false,"raw_author_name":"James Lam","raw_affiliation_strings":["Department of Mechanical Engineering, University of Hong Kong, Pokfulam, Hong Kong"],"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, University of Hong Kong, Pokfulam, Hong Kong","institution_ids":["https://openalex.org/I889458895"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5017887363"],"corresponding_institution_ids":["https://openalex.org/I9842412"],"apc_list":null,"apc_paid":null,"fwci":1.5107,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.82018861,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":98},"biblio":{"volume":"67","issue":"6","first_page":"3005","last_page":"3012"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.9993000030517578,"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/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.9993000030517578,"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/T10621","display_name":"Gene Regulatory Network Analysis","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.9987999796867371,"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/orthant","display_name":"Orthant","score":0.8584975004196167},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7755533456802368},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.7408218383789062},{"id":"https://openalex.org/keywords/separable-space","display_name":"Separable space","score":0.6267523765563965},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.5131471753120422},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.5039870142936707},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.4817209839820862},{"id":"https://openalex.org/keywords/ellipsoid","display_name":"Ellipsoid","score":0.45360928773880005},{"id":"https://openalex.org/keywords/positive-systems","display_name":"Positive systems","score":0.4138838052749634},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3772636950016022},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.36797332763671875},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1182955801486969},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.0951804518699646},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.09334039688110352},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.07674238085746765},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.06374117732048035}],"concepts":[{"id":"https://openalex.org/C2780016784","wikidata":"https://www.wikidata.org/wiki/Q2714507","display_name":"Orthant","level":2,"score":0.8584975004196167},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7755533456802368},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.7408218383789062},{"id":"https://openalex.org/C70710897","wikidata":"https://www.wikidata.org/wiki/Q680081","display_name":"Separable space","level":2,"score":0.6267523765563965},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5131471753120422},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.5039870142936707},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.4817209839820862},{"id":"https://openalex.org/C57489055","wikidata":"https://www.wikidata.org/wiki/Q190046","display_name":"Ellipsoid","level":2,"score":0.45360928773880005},{"id":"https://openalex.org/C2778299942","wikidata":"https://www.wikidata.org/wiki/Q7233296","display_name":"Positive systems","level":3,"score":0.4138838052749634},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3772636950016022},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.36797332763671875},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1182955801486969},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.0951804518699646},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.09334039688110352},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.07674238085746765},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.06374117732048035},{"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/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tac.2021.3088810","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2021.3088810","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"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W615876487","https://openalex.org/W1536762869","https://openalex.org/W1552488793","https://openalex.org/W1750334595","https://openalex.org/W1979098741","https://openalex.org/W1997082542","https://openalex.org/W2008464444","https://openalex.org/W2021660994","https://openalex.org/W2035269147","https://openalex.org/W2058221907","https://openalex.org/W2087464688","https://openalex.org/W2097061644","https://openalex.org/W2113377036","https://openalex.org/W2140214428","https://openalex.org/W2147439098","https://openalex.org/W2155039147","https://openalex.org/W2175431616","https://openalex.org/W2180358230","https://openalex.org/W2259652236","https://openalex.org/W2344594675","https://openalex.org/W2573692685","https://openalex.org/W2610279013","https://openalex.org/W2793550528","https://openalex.org/W2795950123","https://openalex.org/W2805199031","https://openalex.org/W2963716017","https://openalex.org/W2964136943","https://openalex.org/W3104452722","https://openalex.org/W4235143360"],"related_works":["https://openalex.org/W2220253973","https://openalex.org/W1905581482","https://openalex.org/W2991666192","https://openalex.org/W2000898041","https://openalex.org/W2131032422","https://openalex.org/W3186957793","https://openalex.org/W2186188480","https://openalex.org/W2968514504","https://openalex.org/W2372280177","https://openalex.org/W3203676140"],"abstract_inverted_index":{"This":[0,103],"article":[1],"addresses":[2],"the":[3,7,21,34,39,59,69,100,108,123,133,136],"problem":[4,49],"of":[5,9,11,23,36,43,54,72,135],"estimating":[6],"domain":[8,35],"attraction":[10,37],"positive":[12,81],"systems":[13],"under":[14],"a":[15,83,91,94,113,127],"saturated":[16,25],"linear":[17,26],"feedback.":[18],"Compared":[19],"with":[20,140],"analysis":[22],"general":[24],"systems,":[27],"one":[28],"remarkable":[29],"difference":[30],"is":[31,42,86,96,105],"that":[32,90,122],"only":[33],"inside":[38],"first":[40,60],"orthant":[41],"interest.":[44],"Hence,":[45],"we":[46,118],"tackle":[47],"this":[48],"by":[50],"exploiting":[51],"different":[52],"shapes":[53],"invariant":[55,98,129,145],"sets":[56,71],"confined":[57],"in":[58,138],"orthant,":[61],"including":[62],"hyperpyramids":[63],"and":[64,74],"hyperrectangles,":[65],"which":[66],"are,":[67],"respectively,":[68],"level":[70],"sum-separable":[73],"max-separable":[75],"Lyapunov":[76],"functions.":[77],"For":[78],"an":[79],"open-loop":[80,116],"system,":[82],"sufficient":[84],"condition":[85,104],"given":[87],"to":[88],"ensure":[89],"pyramid":[92],"(or":[93],"hyperrectangle)":[95],"contractively":[97],"for":[99,107,112],"closed":[101,124],"loop.":[102],"nonconservative":[106],"single-input":[109],"case.":[110],"Moreover,":[111],"system":[114],"without":[115],"positivity,":[117],"establish":[119],"conditions":[120],"such":[121],"loop":[125],"has":[126],"hyperrectangular":[128],"set.":[130],"Examples":[131],"show":[132],"superiority":[134],"results,":[137],"comparison":[139],"those":[141],"existing":[142],"ones":[143],"using":[144],"ellipsoids.":[146]},"counts_by_year":[{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
