{"id":"https://openalex.org/W3007455401","doi":"https://doi.org/10.23919/ecc51009.2020.9143862","title":"Normal forms of matrix words for stability analysis of discrete-time switched linear systems","display_name":"Normal forms of matrix words for stability analysis of discrete-time switched linear systems","publication_year":2020,"publication_date":"2020-05-01","ids":{"openalex":"https://openalex.org/W3007455401","doi":"https://doi.org/10.23919/ecc51009.2020.9143862","mag":"3007455401"},"language":"en","primary_location":{"id":"doi:10.23919/ecc51009.2020.9143862","is_oa":false,"landing_page_url":"https://doi.org/10.23919/ecc51009.2020.9143862","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2020 European Control Conference (ECC)","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hal.science/hal-02069712/document","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5016694492","display_name":"Cyrille Chenavier","orcid":null},"institutions":[{"id":"https://openalex.org/I2279609970","display_name":"Universit\u00e9 de Lille","ror":"https://ror.org/02kzqn938","country_code":"FR","type":"education","lineage":["https://openalex.org/I2279609970"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210115519","display_name":"Centre de Recherche en Informatique","ror":"https://ror.org/020cdve92","country_code":"FR","type":"facility","lineage":["https://openalex.org/I190752583","https://openalex.org/I2746051580","https://openalex.org/I4210091621","https://openalex.org/I4210115519","https://openalex.org/I70768539"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Cyrille Chenavier","raw_affiliation_strings":["UMR 9189 -CRIStAL - Centre de Recherche en Informatique Signal et Automatique de Lille, Inria, Univ. Lille, CNRS, Lille, France"],"affiliations":[{"raw_affiliation_string":"UMR 9189 -CRIStAL - Centre de Recherche en Informatique Signal et Automatique de Lille, Inria, Univ. Lille, CNRS, Lille, France","institution_ids":["https://openalex.org/I4210115519","https://openalex.org/I2279609970","https://openalex.org/I1294671590"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5041977418","display_name":"Rosane Ushirobira","orcid":"https://orcid.org/0000-0001-9758-5743"},"institutions":[{"id":"https://openalex.org/I4210115519","display_name":"Centre de Recherche en Informatique","ror":"https://ror.org/020cdve92","country_code":"FR","type":"facility","lineage":["https://openalex.org/I190752583","https://openalex.org/I2746051580","https://openalex.org/I4210091621","https://openalex.org/I4210115519","https://openalex.org/I70768539"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I2279609970","display_name":"Universit\u00e9 de Lille","ror":"https://ror.org/02kzqn938","country_code":"FR","type":"education","lineage":["https://openalex.org/I2279609970"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Rosane Ushirobira","raw_affiliation_strings":["UMR 9189 -CRIStAL - Centre de Recherche en Informatique Signal et Automatique de Lille, Inria, Univ. Lille, CNRS, Lille, France"],"affiliations":[{"raw_affiliation_string":"UMR 9189 -CRIStAL - Centre de Recherche en Informatique Signal et Automatique de Lille, Inria, Univ. Lille, CNRS, Lille, France","institution_ids":["https://openalex.org/I4210115519","https://openalex.org/I2279609970","https://openalex.org/I1294671590"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5007994353","display_name":"Laurentiu Hetel","orcid":"https://orcid.org/0000-0001-8445-7881"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I2279609970","display_name":"Universit\u00e9 de Lille","ror":"https://ror.org/02kzqn938","country_code":"FR","type":"education","lineage":["https://openalex.org/I2279609970"]},{"id":"https://openalex.org/I4210115519","display_name":"Centre de Recherche en Informatique","ror":"https://ror.org/020cdve92","country_code":"FR","type":"facility","lineage":["https://openalex.org/I190752583","https://openalex.org/I2746051580","https://openalex.org/I4210091621","https://openalex.org/I4210115519","https://openalex.org/I70768539"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Laurentiu Hetel","raw_affiliation_strings":["UMR 9189 - CRIStAL - Centre de Recherche en Informatique Signal et Automatique de Lille, CNRS, Univ. Lille, Lille, France"],"affiliations":[{"raw_affiliation_string":"UMR 9189 - CRIStAL - Centre de Recherche en Informatique Signal et Automatique de Lille, CNRS, Univ. Lille, Lille, France","institution_ids":["https://openalex.org/I4210115519","https://openalex.org/I2279609970","https://openalex.org/I1294671590"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5016694492"],"corresponding_institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I2279609970","https://openalex.org/I4210115519"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.01934883,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"1842","last_page":"1846"},"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":0.9997000098228455,"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":0.9997000098228455,"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/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.9951000213623047,"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/T11125","display_name":"Petri Nets in System Modeling","score":0.9911999702453613,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6627129316329956},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.6360332369804382},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.623075008392334},{"id":"https://openalex.org/keywords/exponential-stability","display_name":"Exponential stability","score":0.5457108616828918},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5320430994033813},{"id":"https://openalex.org/keywords/matrix-exponential","display_name":"Matrix exponential","score":0.5031082034111023},{"id":"https://openalex.org/keywords/matrix-analysis","display_name":"Matrix analysis","score":0.494214802980423},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.4769510328769684},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4648095369338989},{"id":"https://openalex.org/keywords/state-transition-matrix","display_name":"State-transition matrix","score":0.43735504150390625},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.4198119342327118},{"id":"https://openalex.org/keywords/symmetric-matrix","display_name":"Symmetric matrix","score":0.4160904884338379},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2312752902507782},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.17072364687919617},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.10493743419647217}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6627129316329956},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.6360332369804382},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.623075008392334},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.5457108616828918},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5320430994033813},{"id":"https://openalex.org/C195906000","wikidata":"https://www.wikidata.org/wiki/Q1191722","display_name":"Matrix exponential","level":3,"score":0.5031082034111023},{"id":"https://openalex.org/C149488123","wikidata":"https://www.wikidata.org/wiki/Q17098730","display_name":"Matrix analysis","level":3,"score":0.494214802980423},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.4769510328769684},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4648095369338989},{"id":"https://openalex.org/C22629506","wikidata":"https://www.wikidata.org/wiki/Q7602993","display_name":"State-transition matrix","level":4,"score":0.43735504150390625},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.4198119342327118},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.4160904884338379},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2312752902507782},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.17072364687919617},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.10493743419647217},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.0},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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},{"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:10.23919/ecc51009.2020.9143862","is_oa":false,"landing_page_url":"https://doi.org/10.23919/ecc51009.2020.9143862","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2020 European Control Conference (ECC)","raw_type":"proceedings-article"},{"id":"pmh:oai:HAL:hal-02069712v3","is_oa":true,"landing_page_url":"https://hal.science/hal-02069712","pdf_url":"https://hal.science/hal-02069712/document","source":{"id":"https://openalex.org/S4406922461","display_name":"SPIRE - Sciences Po Institutional REpository","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":"ECC 2020 - 18th European Control Conference, May 2020, Saint Petersburg, Russia. ⟨10.23919/ECC51009.2020.9143862⟩","raw_type":"Conference papers"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-02069712v3","is_oa":true,"landing_page_url":"https://hal.science/hal-02069712","pdf_url":"https://hal.science/hal-02069712/document","source":{"id":"https://openalex.org/S4406922461","display_name":"SPIRE - Sciences Po Institutional REpository","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":"ECC 2020 - 18th European Control Conference, May 2020, Saint Petersburg, Russia. ⟨10.23919/ECC51009.2020.9143862⟩","raw_type":"Conference papers"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3007455401.pdf","grobid_xml":"https://content.openalex.org/works/W3007455401.grobid-xml"},"referenced_works_count":23,"referenced_works":["https://openalex.org/W1642990561","https://openalex.org/W1938883640","https://openalex.org/W1978587117","https://openalex.org/W1981518949","https://openalex.org/W1991656001","https://openalex.org/W2003652915","https://openalex.org/W2025733943","https://openalex.org/W2029508229","https://openalex.org/W2042741865","https://openalex.org/W2057541071","https://openalex.org/W2076566814","https://openalex.org/W2084970142","https://openalex.org/W2111394600","https://openalex.org/W2116680678","https://openalex.org/W2118863844","https://openalex.org/W2143181390","https://openalex.org/W2147741811","https://openalex.org/W2155689575","https://openalex.org/W2158453457","https://openalex.org/W2168726075","https://openalex.org/W2544001552","https://openalex.org/W2591198617","https://openalex.org/W2901588109"],"related_works":["https://openalex.org/W1984232695","https://openalex.org/W120389515","https://openalex.org/W2009187315","https://openalex.org/W4210551724","https://openalex.org/W2017295304","https://openalex.org/W27112594","https://openalex.org/W2071296300","https://openalex.org/W2102959691","https://openalex.org/W76867408","https://openalex.org/W2970525929"],"abstract_inverted_index":{"In":[0,69],"this":[1,58,101],"paper,":[2],"we":[3,71,103],"propose":[4],"a":[5,73],"new":[6],"method":[7,51],"for":[8],"investigating":[9],"the":[10,31,48,55,78,98],"stability":[11,24,62,107,110],"of":[12,19,25,33,35,45,47,60,80,111],"discrete-time":[13],"switched":[14,113],"linear":[15,20,36,64,81],"systems":[16,27],"by":[17,40,84,91],"means":[18],"algebra":[21],"techniques.":[22],"Exponential":[23],"such":[26],"is":[28,89,117],"equivalent":[29],"to":[30,75,108,119],"existence":[32],"solutions":[34],"matrix":[37,41,67,82,93],"inequalities":[38],"indexed":[39],"words":[42,94],"(i.e.":[43],"products":[44],"matrices":[46],"sub-systems).":[49],"Our":[50],"consists":[52],"in":[53],"using":[54],"link":[56],"between":[57],"characterization":[59],"exponential":[61,106],"and":[63],"dependency":[65],"among":[66],"words.":[68],"particular,":[70],"introduce":[72],"criterion":[74],"reduce":[76],"drastically":[77],"number":[79],"inequalities,":[83],"removing":[85],"redundant":[86],"ones.":[87],"This":[88],"achieved":[90],"eliminating":[92],"that":[95],"depend":[96],"on":[97],"others.":[99],"From":[100],"criterion,":[102],"also":[104],"relate":[105],"quadratic":[109],"another":[112],"system.":[114],"An":[115],"example":[116],"given":[118],"illustrate":[120],"our":[121],"methods.":[122]},"counts_by_year":[],"updated_date":"2026-03-22T08:09:32.410652","created_date":"2025-10-10T00:00:00"}