{"id":"https://openalex.org/W2012829100","doi":"https://doi.org/10.1109/acc.2012.6315204","title":"Synthesis of polynomial static state feedback laws and analysis for discrete-time polynomial systems with saturating inputs","display_name":"Synthesis of polynomial static state feedback laws and analysis for discrete-time polynomial systems with saturating inputs","publication_year":2012,"publication_date":"2012-06-01","ids":{"openalex":"https://openalex.org/W2012829100","doi":"https://doi.org/10.1109/acc.2012.6315204","mag":"2012829100"},"language":"en","primary_location":{"id":"doi:10.1109/acc.2012.6315204","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2012.6315204","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 American Control Conference (ACC)","raw_type":"proceedings-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/A5066966226","display_name":"Gi\u00f3rgio Valm\u00f3rbida","orcid":"https://orcid.org/0000-0002-1710-8590"},"institutions":[{"id":"https://openalex.org/I134560555","display_name":"Universit\u00e9 Toulouse III - Paul Sabatier","ror":"https://ror.org/02v6kpv12","country_code":"FR","type":"education","lineage":["https://openalex.org/I134560555","https://openalex.org/I4405258862"]},{"id":"https://openalex.org/I17866349","display_name":"Universit\u00e9 F\u00e9d\u00e9rale de Toulouse Midi-Pyr\u00e9n\u00e9es","ror":"https://ror.org/004raaa70","country_code":"FR","type":"education","lineage":["https://openalex.org/I17866349"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I190497903","display_name":"Laboratoire d'Analyse et d'Architecture des Syst\u00e8mes","ror":"https://ror.org/03vcm6439","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I134560555","https://openalex.org/I190497903","https://openalex.org/I196454796","https://openalex.org/I205747304","https://openalex.org/I205747304","https://openalex.org/I4210095849","https://openalex.org/I4210159245","https://openalex.org/I4387153255","https://openalex.org/I4405258862","https://openalex.org/I4405258862","https://openalex.org/I4405258862","https://openalex.org/I4405258862"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"G. Valmorbida","raw_affiliation_strings":["LAAS, CNRS, Toulouse, France","UPS, INSA, INP, ISAE ; UT1, UTM, LAAS, Universit\u00e9 de Toulouse, Toulouse, France","UT1, UTM, LAAS, Universit\u00e9 de Toulouse, Toulouse, France","UPS, INSA, INP, ISAE"],"affiliations":[{"raw_affiliation_string":"LAAS, CNRS, Toulouse, France","institution_ids":["https://openalex.org/I190497903","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"UPS, INSA, INP, ISAE ; UT1, UTM, LAAS, Universit\u00e9 de Toulouse, Toulouse, France","institution_ids":["https://openalex.org/I134560555","https://openalex.org/I17866349","https://openalex.org/I190497903"]},{"raw_affiliation_string":"UT1, UTM, LAAS, Universit\u00e9 de Toulouse, Toulouse, France","institution_ids":["https://openalex.org/I17866349","https://openalex.org/I190497903"]},{"raw_affiliation_string":"UPS, INSA, INP, ISAE","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5106471543","display_name":"S. Tarbouriech","orcid":null},"institutions":[{"id":"https://openalex.org/I190497903","display_name":"Laboratoire d'Analyse et d'Architecture des Syst\u00e8mes","ror":"https://ror.org/03vcm6439","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I134560555","https://openalex.org/I190497903","https://openalex.org/I196454796","https://openalex.org/I205747304","https://openalex.org/I205747304","https://openalex.org/I4210095849","https://openalex.org/I4210159245","https://openalex.org/I4387153255","https://openalex.org/I4405258862","https://openalex.org/I4405258862","https://openalex.org/I4405258862","https://openalex.org/I4405258862"]},{"id":"https://openalex.org/I17866349","display_name":"Universit\u00e9 F\u00e9d\u00e9rale de Toulouse Midi-Pyr\u00e9n\u00e9es","ror":"https://ror.org/004raaa70","country_code":"FR","type":"education","lineage":["https://openalex.org/I17866349"]},{"id":"https://openalex.org/I134560555","display_name":"Universit\u00e9 Toulouse III - Paul Sabatier","ror":"https://ror.org/02v6kpv12","country_code":"FR","type":"education","lineage":["https://openalex.org/I134560555","https://openalex.org/I4405258862"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"S. Tarbouriech","raw_affiliation_strings":["LAAS, CNRS, Toulouse, France","UPS, INSA, INP, ISAE ; UT1, UTM, LAAS, Universit\u00e9 de Toulouse, Toulouse, France","UPS, INSA, INP, ISAE","UT1, UTM, LAAS, Universit\u00e9 de Toulouse, Toulouse, France"],"affiliations":[{"raw_affiliation_string":"LAAS, CNRS, Toulouse, France","institution_ids":["https://openalex.org/I190497903","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"UPS, INSA, INP, ISAE ; UT1, UTM, LAAS, Universit\u00e9 de Toulouse, Toulouse, France","institution_ids":["https://openalex.org/I134560555","https://openalex.org/I17866349","https://openalex.org/I190497903"]},{"raw_affiliation_string":"UPS, INSA, INP, ISAE","institution_ids":[]},{"raw_affiliation_string":"UT1, UTM, LAAS, Universit\u00e9 de Toulouse, Toulouse, France","institution_ids":["https://openalex.org/I17866349","https://openalex.org/I190497903"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047274896","display_name":"Germain Garc\u00eda","orcid":"https://orcid.org/0000-0002-7147-5105"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I134560555","display_name":"Universit\u00e9 Toulouse III - Paul Sabatier","ror":"https://ror.org/02v6kpv12","country_code":"FR","type":"education","lineage":["https://openalex.org/I134560555","https://openalex.org/I4405258862"]},{"id":"https://openalex.org/I190497903","display_name":"Laboratoire d'Analyse et d'Architecture des Syst\u00e8mes","ror":"https://ror.org/03vcm6439","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I134560555","https://openalex.org/I190497903","https://openalex.org/I196454796","https://openalex.org/I205747304","https://openalex.org/I205747304","https://openalex.org/I4210095849","https://openalex.org/I4210159245","https://openalex.org/I4387153255","https://openalex.org/I4405258862","https://openalex.org/I4405258862","https://openalex.org/I4405258862","https://openalex.org/I4405258862"]},{"id":"https://openalex.org/I17866349","display_name":"Universit\u00e9 F\u00e9d\u00e9rale de Toulouse Midi-Pyr\u00e9n\u00e9es","ror":"https://ror.org/004raaa70","country_code":"FR","type":"education","lineage":["https://openalex.org/I17866349"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"G. Garcia","raw_affiliation_strings":["LAAS, CNRS, Toulouse, France","UPS, INSA, INP, ISAE ; UT1, UTM, LAAS, Universit\u00e9 de Toulouse, Toulouse, France","UT1, UTM, LAAS, Universit\u00e9 de Toulouse, Toulouse, France","UPS, INSA, INP, ISAE"],"affiliations":[{"raw_affiliation_string":"LAAS, CNRS, Toulouse, France","institution_ids":["https://openalex.org/I190497903","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"UPS, INSA, INP, ISAE ; UT1, UTM, LAAS, Universit\u00e9 de Toulouse, Toulouse, France","institution_ids":["https://openalex.org/I134560555","https://openalex.org/I17866349","https://openalex.org/I190497903"]},{"raw_affiliation_string":"UT1, UTM, LAAS, Universit\u00e9 de Toulouse, Toulouse, France","institution_ids":["https://openalex.org/I17866349","https://openalex.org/I190497903"]},{"raw_affiliation_string":"UPS, INSA, INP, ISAE","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5023173503","display_name":"Luca Zaccarian","orcid":"https://orcid.org/0000-0003-1247-0029"},"institutions":[{"id":"https://openalex.org/I17866349","display_name":"Universit\u00e9 F\u00e9d\u00e9rale de Toulouse Midi-Pyr\u00e9n\u00e9es","ror":"https://ror.org/004raaa70","country_code":"FR","type":"education","lineage":["https://openalex.org/I17866349"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I134560555","display_name":"Universit\u00e9 Toulouse III - Paul Sabatier","ror":"https://ror.org/02v6kpv12","country_code":"FR","type":"education","lineage":["https://openalex.org/I134560555","https://openalex.org/I4405258862"]},{"id":"https://openalex.org/I190497903","display_name":"Laboratoire d'Analyse et d'Architecture des Syst\u00e8mes","ror":"https://ror.org/03vcm6439","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I134560555","https://openalex.org/I190497903","https://openalex.org/I196454796","https://openalex.org/I205747304","https://openalex.org/I205747304","https://openalex.org/I4210095849","https://openalex.org/I4210159245","https://openalex.org/I4387153255","https://openalex.org/I4405258862","https://openalex.org/I4405258862","https://openalex.org/I4405258862","https://openalex.org/I4405258862"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"L. Zaccarian","raw_affiliation_strings":["LAAS, CNRS, Toulouse, France","UPS, INSA, INP, ISAE ; UT1, UTM, LAAS, Universit\u00e9 de Toulouse, Toulouse, France","UPS, INSA, INP, ISAE","UT1, UTM, LAAS, Universit\u00e9 de Toulouse, Toulouse, France"],"affiliations":[{"raw_affiliation_string":"LAAS, CNRS, Toulouse, France","institution_ids":["https://openalex.org/I190497903","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"UPS, INSA, INP, ISAE ; UT1, UTM, LAAS, Universit\u00e9 de Toulouse, Toulouse, France","institution_ids":["https://openalex.org/I134560555","https://openalex.org/I17866349","https://openalex.org/I190497903"]},{"raw_affiliation_string":"UPS, INSA, INP, ISAE","institution_ids":[]},{"raw_affiliation_string":"UT1, UTM, LAAS, Universit\u00e9 de Toulouse, Toulouse, France","institution_ids":["https://openalex.org/I17866349","https://openalex.org/I190497903"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5066966226"],"corresponding_institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I134560555","https://openalex.org/I17866349","https://openalex.org/I190497903"],"apc_list":null,"apc_paid":null,"fwci":0.563,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.72829103,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"390","issue":null,"first_page":"2325","last_page":"2330"},"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":0.9976000189781189,"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":0.9976000189781189,"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":0.9861999750137329,"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/T14083","display_name":"Extremum Seeking Control Systems","score":0.9843999743461609,"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/polynomial","display_name":"Polynomial","score":0.6892864108085632},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.683023989200592},{"id":"https://openalex.org/keywords/kharitonovs-theorem","display_name":"Kharitonov's theorem","score":0.6435353755950928},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5772402882575989},{"id":"https://openalex.org/keywords/stable-polynomial","display_name":"Stable polynomial","score":0.520341157913208},{"id":"https://openalex.org/keywords/matrix-polynomial","display_name":"Matrix polynomial","score":0.5018808841705322},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.4612736701965332},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.39692187309265137},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.38595446944236755},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.21227604150772095},{"id":"https://openalex.org/keywords/alternating-polynomial","display_name":"Alternating polynomial","score":0.19466307759284973},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.17041724920272827},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.15680432319641113},{"id":"https://openalex.org/keywords/square-free-polynomial","display_name":"Square-free polynomial","score":0.15625381469726562},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.13383066654205322},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.059718310832977295}],"concepts":[{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.6892864108085632},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.683023989200592},{"id":"https://openalex.org/C173047080","wikidata":"https://www.wikidata.org/wiki/Q6400676","display_name":"Kharitonov's theorem","level":5,"score":0.6435353755950928},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5772402882575989},{"id":"https://openalex.org/C45025165","wikidata":"https://www.wikidata.org/wiki/Q13424738","display_name":"Stable polynomial","level":5,"score":0.520341157913208},{"id":"https://openalex.org/C101044782","wikidata":"https://www.wikidata.org/wiki/Q6787887","display_name":"Matrix polynomial","level":3,"score":0.5018808841705322},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.4612736701965332},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.39692187309265137},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.38595446944236755},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.21227604150772095},{"id":"https://openalex.org/C170412648","wikidata":"https://www.wikidata.org/wiki/Q4736415","display_name":"Alternating polynomial","level":4,"score":0.19466307759284973},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.17041724920272827},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.15680432319641113},{"id":"https://openalex.org/C101525915","wikidata":"https://www.wikidata.org/wiki/Q7581979","display_name":"Square-free polynomial","level":4,"score":0.15625381469726562},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.13383066654205322},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.059718310832977295},{"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/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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/acc.2012.6315204","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2012.6315204","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 American Control Conference (ACC)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","score":0.7799999713897705,"display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1600295805","https://openalex.org/W1999913571","https://openalex.org/W2056633109","https://openalex.org/W2060458267","https://openalex.org/W2068338643","https://openalex.org/W2116586985","https://openalex.org/W2133404041","https://openalex.org/W2137470393","https://openalex.org/W2146586176","https://openalex.org/W2167019375","https://openalex.org/W2182510773","https://openalex.org/W2491336180","https://openalex.org/W2536620281","https://openalex.org/W3210839039"],"related_works":["https://openalex.org/W2980589713","https://openalex.org/W2149734642","https://openalex.org/W4311251537","https://openalex.org/W4320917455","https://openalex.org/W1984887342","https://openalex.org/W3216258873","https://openalex.org/W2015410487","https://openalex.org/W1971813609","https://openalex.org/W2365733060","https://openalex.org/W2131967299"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"we":[3],"provide":[4],"conditions":[5,21,30],"for":[6,16,22],"the":[7,23,39,45,48,57,67,88,94,99,111],"synthesis":[8],"of":[9,26,47,56,69,86,96,98,110],"polynomial":[10,18,34,49,63,89,112],"static":[11],"state":[12],"feedback":[13],"control":[14,51,90],"laws":[15,91],"discrete-time":[17],"systems":[19],"and":[20,43,92],"stability":[24,54],"analysis":[25,55],"input-saturating":[27],"systems.":[28],"These":[29],"are":[31,103],"based":[32],"on":[33],"inequalities":[35],"affine":[36],"both":[37],"in":[38,44],"Lyapunov":[40,64],"function":[41],"parameters":[42],"gains":[46],"state-feedback":[50],"law.":[52],"The":[53,84],"saturating":[58],"system":[59,102],"is":[60],"performed":[61],"with":[62,66],"functions":[65],"help":[68],"a":[70],"generalized":[71],"sector":[72],"condition":[73],"which":[74],"allows":[75],"us":[76],"to":[77],"take":[78],"into":[79],"account":[80],"nonsymmetric":[81],"saturation":[82],"bounds.":[83],"problems":[85],"computing":[87],"estimating":[93],"region":[95],"attraction":[97],"resulting":[100],"closed-loop":[101],"solved":[104],"numerically":[105],"by":[106],"considering":[107],"sum-of-squares":[108],"relaxations":[109],"inequalities.":[113]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2017,"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"}
