{"id":"https://openalex.org/W1995454290","doi":"https://doi.org/10.1137/s0363012999365704","title":"Lie-Algebraic Stability Criteria for Switched Systems","display_name":"Lie-Algebraic Stability Criteria for Switched Systems","publication_year":2001,"publication_date":"2001-01-01","ids":{"openalex":"https://openalex.org/W1995454290","doi":"https://doi.org/10.1137/s0363012999365704","mag":"1995454290"},"language":"en","primary_location":{"id":"doi:10.1137/s0363012999365704","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0363012999365704","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"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 Control and Optimization","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/A5086178969","display_name":"Andrei Agrachev","orcid":null},"institutions":[{"id":"https://openalex.org/I2801160905","display_name":"Steklov Mathematical Institute","ror":"https://ror.org/03zeg8w71","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I2801160905","https://openalex.org/I4210124601"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Andrei A. Agrachev","raw_affiliation_strings":["RAS - Steklov Mathematical Institute"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"RAS - Steklov Mathematical Institute","institution_ids":["https://openalex.org/I2801160905"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5086321981","display_name":"Daniel Liberzon","orcid":"https://orcid.org/0000-0003-2383-0114"},"institutions":[{"id":"https://openalex.org/I4400573203","display_name":"Nature Inspires Creativity Engineers Lab","ror":"https://ror.org/02bczqy30","country_code":null,"type":"facility","lineage":["https://openalex.org/I201841394","https://openalex.org/I4400573203"]}],"countries":[],"is_corresponding":false,"raw_author_name":"Daniel Liberzon","raw_affiliation_strings":["Coordinated Science Lab"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Coordinated Science Lab","institution_ids":["https://openalex.org/I4400573203"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":43.2399,"has_fulltext":false,"cited_by_count":339,"citation_normalized_percentile":{"value":0.99861465,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"40","issue":"1","first_page":"253","last_page":"269"},"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":0.9994999766349792,"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":0.9994999766349792,"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":0.9973999857902527,"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/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.988099992275238,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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":0.9038099050521851},{"id":"https://openalex.org/keywords/lie-algebra","display_name":"Lie algebra","score":0.6650072336196899},{"id":"https://openalex.org/keywords/subalgebra","display_name":"Subalgebra","score":0.5998246669769287},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5290179252624512},{"id":"https://openalex.org/keywords/adjoint-representation","display_name":"Adjoint representation","score":0.47104835510253906},{"id":"https://openalex.org/keywords/ideal","display_name":"Ideal (ethics)","score":0.4662799835205078},{"id":"https://openalex.org/keywords/lie-group","display_name":"Lie group","score":0.4558405578136444},{"id":"https://openalex.org/keywords/lie-conformal-algebra","display_name":"Lie conformal algebra","score":0.4487265646457672},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.43917179107666016},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.43517422676086426},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4350026547908783},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.4240865707397461},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.3209553360939026},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1763594150543213}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9038099050521851},{"id":"https://openalex.org/C51568863","wikidata":"https://www.wikidata.org/wiki/Q664495","display_name":"Lie algebra","level":2,"score":0.6650072336196899},{"id":"https://openalex.org/C67996461","wikidata":"https://www.wikidata.org/wiki/Q629933","display_name":"Subalgebra","level":3,"score":0.5998246669769287},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5290179252624512},{"id":"https://openalex.org/C58910974","wikidata":"https://www.wikidata.org/wiki/Q1017106","display_name":"Adjoint representation","level":3,"score":0.47104835510253906},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.4662799835205078},{"id":"https://openalex.org/C187915474","wikidata":"https://www.wikidata.org/wiki/Q622679","display_name":"Lie group","level":2,"score":0.4558405578136444},{"id":"https://openalex.org/C73648015","wikidata":"https://www.wikidata.org/wiki/Q6543817","display_name":"Lie conformal algebra","level":3,"score":0.4487265646457672},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.43917179107666016},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.43517422676086426},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4350026547908783},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.4240865707397461},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.3209553360939026},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1763594150543213},{"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/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/s0363012999365704","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0363012999365704","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"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 Control and Optimization","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.23.2450","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.23.2450","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://black.csl.uiuc.edu/~liberzon/research/agrachev.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.35.7824","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.35.7824","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://pantheon.yale.edu/~dml33/agrachev.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.589.822","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.589.822","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ece.ubc.ca/~moishi/eece571m/articles/Liberzon01.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W106573161","https://openalex.org/W1491730507","https://openalex.org/W1525184094","https://openalex.org/W1563446057","https://openalex.org/W1592648094","https://openalex.org/W1891321725","https://openalex.org/W1978587117","https://openalex.org/W1995063858","https://openalex.org/W2006008643","https://openalex.org/W2029112850","https://openalex.org/W2029641002","https://openalex.org/W2076566814","https://openalex.org/W2125335329","https://openalex.org/W2128978199","https://openalex.org/W2133448423","https://openalex.org/W2138126116","https://openalex.org/W2143181390","https://openalex.org/W2145511008","https://openalex.org/W2146018367","https://openalex.org/W2154510168","https://openalex.org/W4206042551","https://openalex.org/W4293078920"],"related_works":["https://openalex.org/W3005162266","https://openalex.org/W4297797709","https://openalex.org/W2565931874","https://openalex.org/W4298401637","https://openalex.org/W2940979654","https://openalex.org/W3133248316","https://openalex.org/W2963288691","https://openalex.org/W2037832882","https://openalex.org/W2460513362","https://openalex.org/W1569557269"],"abstract_inverted_index":{"It":[0],"was":[1],"recently":[2],"shown":[3],"that":[4,27,44,53,94,117],"a":[5,15,20,65,68,72,75,96,111],"family":[6,112],"of":[7,67,113,131,139],"exponentially":[8,34],"stable":[9,35,114],"linear":[10,31,121],"systems":[11,87],"whose":[12],"matrices":[13,60,115],"generate":[14],"solvable":[16,69],"Lie":[17,55,77,97,132],"algebra":[18,56,98],"possesses":[19],"quadratic":[21],"common":[22],"Lyapunov":[23],"function,":[24],"which":[25],"implies":[26],"the":[28,45,50,54,102,118,129,137,140],"corresponding":[29,80,119],"switched":[30,86,120],"system":[32,122],"is":[33,88,123],"for":[36,84,142],"arbitrary":[37],"switching.":[38],"In":[39],"this":[40],"paper":[41,141],"we":[42,92],"prove":[43],"same":[46],"properties":[47],"hold":[48],"under":[49],"weaker":[51],"condition":[52],"generated":[57,109],"by":[58,110],"given":[59],"can":[61,107],"be":[62,108],"decomposed":[63],"into":[64],"sum":[66],"ideal":[70],"and":[71],"subalgebra":[73],"with":[74],"compact":[76],"group.":[78],"The":[79],"local":[81],"stability":[82],"result":[83],"nonlinear":[85],"also":[89],"established.":[90],"Moreover,":[91],"demonstrate":[93],"if":[95],"fails":[99],"to":[100],"satisfy":[101],"above":[103],"condition,":[104],"then":[105],"it":[106],"such":[116],"not":[124],"stable.":[125],"Relevant":[126],"facts":[127],"from":[128],"theory":[130],"algebras":[133],"are":[134],"collected":[135],"at":[136],"end":[138],"easy":[143],"reference.":[144]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":9},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":10},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":10},{"year":2019,"cited_by_count":9},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":9},{"year":2016,"cited_by_count":10},{"year":2015,"cited_by_count":18},{"year":2014,"cited_by_count":10},{"year":2013,"cited_by_count":14},{"year":2012,"cited_by_count":24}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}