{"id":"https://openalex.org/W1996478669","doi":"https://doi.org/10.2478/v10006-007-0036-x","title":"Extended Lie Algebraic Stability Analysis for Switched Systems with Continuous-Time and Discrete-Time Subsystems","display_name":"Extended Lie Algebraic Stability Analysis for Switched Systems with Continuous-Time and Discrete-Time Subsystems","publication_year":2007,"publication_date":"2007-12-01","ids":{"openalex":"https://openalex.org/W1996478669","doi":"https://doi.org/10.2478/v10006-007-0036-x","mag":"1996478669"},"language":"en","primary_location":{"id":"doi:10.2478/v10006-007-0036-x","is_oa":true,"landing_page_url":"https://doi.org/10.2478/v10006-007-0036-x","pdf_url":"https://sciendo.com/pdf/10.2478/v10006-007-0036-x","source":{"id":"https://openalex.org/S117679522","display_name":"International Journal of Applied Mathematics and Computer Science","issn_l":"1641-876X","issn":["1641-876X","2083-8492"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Applied Mathematics and Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://sciendo.com/pdf/10.2478/v10006-007-0036-x","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5046218317","display_name":"Guisheng Zhai","orcid":"https://orcid.org/0000-0001-5073-9485"},"institutions":[{"id":"https://openalex.org/I15807432","display_name":"Osaka Prefecture University","ror":"https://ror.org/02cf1je33","country_code":"JP","type":"education","lineage":["https://openalex.org/I15807432"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Guisheng Zhai","raw_affiliation_strings":["Department of Mechanical Engineering, Osaka Prefecture University, Sakai, Osaka 599-8531, Japan"],"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, Osaka Prefecture University, Sakai, Osaka 599-8531, Japan","institution_ids":["https://openalex.org/I15807432"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5072462741","display_name":"Xuping Xu","orcid":null},"institutions":[{"id":"https://openalex.org/I130769515","display_name":"Pennsylvania State University","ror":"https://ror.org/04p491231","country_code":"US","type":"education","lineage":["https://openalex.org/I130769515"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Xuping Xu","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Penn State Erie, Erie, PA 16563-1701, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Penn State Erie, Erie, PA 16563-1701, USA","institution_ids":["https://openalex.org/I130769515"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045445273","display_name":"Hai Lin","orcid":"https://orcid.org/0000-0002-5242-2366"},"institutions":[{"id":"https://openalex.org/I107639228","display_name":"University of Notre Dame","ror":"https://ror.org/00mkhxb43","country_code":"US","type":"education","lineage":["https://openalex.org/I107639228"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Hai Lin","raw_affiliation_strings":["Department of Electrical Engineering University of Notre Dame Notre Dame, Indiana 46556, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering University of Notre Dame Notre Dame, Indiana 46556, USA","institution_ids":["https://openalex.org/I107639228"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5004057129","display_name":"Derong Liu","orcid":"https://orcid.org/0000-0003-3715-4778"},"institutions":[{"id":"https://openalex.org/I39422238","display_name":"University of Illinois Chicago","ror":"https://ror.org/02mpq6x41","country_code":"US","type":"education","lineage":["https://openalex.org/I39422238"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Derong Liu","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of Illinois at Chicago, Chicago, IL 60607-7053, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Illinois at Chicago, Chicago, IL 60607-7053, USA","institution_ids":["https://openalex.org/I39422238"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5046218317"],"corresponding_institution_ids":["https://openalex.org/I15807432"],"apc_list":{"value":4080,"currency":"PLN","value_usd":1100},"apc_paid":{"value":4080,"currency":"PLN","value_usd":1100},"fwci":0.8778,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.79565009,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"17","issue":"4","first_page":"447","last_page":"454"},"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":0.9998000264167786,"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":0.9998000264167786,"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9940999746322632,"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":0.9940000176429749,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6967570781707764},{"id":"https://openalex.org/keywords/lie-algebra","display_name":"Lie algebra","score":0.6099460124969482},{"id":"https://openalex.org/keywords/dwell-time","display_name":"Dwell time","score":0.5960378050804138},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.545120894908905},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.5449290871620178},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5364865064620972},{"id":"https://openalex.org/keywords/exponential-stability","display_name":"Exponential stability","score":0.5326395034790039},{"id":"https://openalex.org/keywords/discrete-time-and-continuous-time","display_name":"Discrete time and continuous time","score":0.5124712586402893},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.44277650117874146},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.43856751918792725},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4102063477039337},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.37587404251098633},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.19295808672904968},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.15614548325538635}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6967570781707764},{"id":"https://openalex.org/C51568863","wikidata":"https://www.wikidata.org/wiki/Q664495","display_name":"Lie algebra","level":2,"score":0.6099460124969482},{"id":"https://openalex.org/C151637689","wikidata":"https://www.wikidata.org/wiki/Q5318064","display_name":"Dwell time","level":2,"score":0.5960378050804138},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.545120894908905},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5449290871620178},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5364865064620972},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.5326395034790039},{"id":"https://openalex.org/C55689738","wikidata":"https://www.wikidata.org/wiki/Q15963867","display_name":"Discrete time and continuous time","level":2,"score":0.5124712586402893},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.44277650117874146},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.43856751918792725},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4102063477039337},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.37587404251098633},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.19295808672904968},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.15614548325538635},{"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/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C70410870","wikidata":"https://www.wikidata.org/wiki/Q199906","display_name":"Clinical psychology","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.2478/v10006-007-0036-x","is_oa":true,"landing_page_url":"https://doi.org/10.2478/v10006-007-0036-x","pdf_url":"https://sciendo.com/pdf/10.2478/v10006-007-0036-x","source":{"id":"https://openalex.org/S117679522","display_name":"International Journal of Applied Mathematics and Computer Science","issn_l":"1641-876X","issn":["1641-876X","2083-8492"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Applied Mathematics and Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.390.3092","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.390.3092","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://matwbn.icm.edu.pl/ksiazki/amc/amc17/amc1742.pdf","raw_type":"text"},{"id":"pmh:oai:zbc.uz.zgora.pl:78666","is_oa":false,"landing_page_url":"https://zbc.uz.zgora.pl/dlibra/docmetadata?showContent=true&id=78666","pdf_url":null,"source":{"id":"https://openalex.org/S4306400400","display_name":"Digital library of Zielona Gora (University of Zielona G\u00f3ra)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I46305939","host_organization_name":"University of Zielona G\u00f3ra","host_organization_lineage":["https://openalex.org/I46305939"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://www.amcs.uz.zgora.pl/?action=papers&issue=30","raw_type":"artyku\u0142"}],"best_oa_location":{"id":"doi:10.2478/v10006-007-0036-x","is_oa":true,"landing_page_url":"https://doi.org/10.2478/v10006-007-0036-x","pdf_url":"https://sciendo.com/pdf/10.2478/v10006-007-0036-x","source":{"id":"https://openalex.org/S117679522","display_name":"International Journal of Applied Mathematics and Computer Science","issn_l":"1641-876X","issn":["1641-876X","2083-8492"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Applied Mathematics and Computer Science","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320310260","display_name":"University of Notre Dame","ror":"https://ror.org/00mkhxb43"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1996478669.pdf","grobid_xml":"https://content.openalex.org/works/W1996478669.grobid-xml"},"referenced_works_count":19,"referenced_works":["https://openalex.org/W60668364","https://openalex.org/W301328986","https://openalex.org/W1552094772","https://openalex.org/W1563446057","https://openalex.org/W1995063858","https://openalex.org/W1995454290","https://openalex.org/W1995875215","https://openalex.org/W2006144895","https://openalex.org/W2029112850","https://openalex.org/W2029425187","https://openalex.org/W2104958104","https://openalex.org/W2109709801","https://openalex.org/W2142160248","https://openalex.org/W2143181390","https://openalex.org/W2145511008","https://openalex.org/W2147259809","https://openalex.org/W2322637817","https://openalex.org/W2618561253","https://openalex.org/W4244380134"],"related_works":["https://openalex.org/W4280579534","https://openalex.org/W4224312498","https://openalex.org/W2407712845","https://openalex.org/W3068859459","https://openalex.org/W2917177193","https://openalex.org/W1508583995","https://openalex.org/W2981305970","https://openalex.org/W2967346707","https://openalex.org/W2018232565","https://openalex.org/W2055077105"],"abstract_inverted_index":{"Extended":[0],"Lie":[1,31,49,84],"Algebraic":[2],"Stability":[3],"Analysis":[4],"for":[5,16,61,98],"Switched":[6],"Systems":[7],"with":[8],"Continuous-Time":[9],"and":[10,25,47,64,81,101],"Discrete-Time":[11],"Subsystems":[12],"We":[13],"analyze":[14],"stability":[15],"switched":[17,67,103],"systems":[18],"which":[19],"are":[20,44,79,116],"composed":[21],"of":[22],"both":[23],"continuous-time":[24],"discrete-time":[26],"subsystems.":[27],"By":[28],"considering":[29],"a":[30,56,93,109],"algebra":[32,50,85],"generated":[33],"by":[34],"all":[35,42,62,77,99],"subsystem":[36],"matrices,":[37],"we":[38,88],"show":[39,89],"that":[40,90],"if":[41],"subsystems":[43,63,78,100],"Hurwitz/Schur":[45],"stable":[46,71,80,107],"this":[48],"is":[51,55,69,86,92,105],"solvable,":[52,87],"then":[53],"there":[54,91],"common":[57,94],"quadratic":[58,95],"Lyapunov":[59],"function":[60,97],"thus":[65],"the":[66,82,102,120],"system":[68,104],"exponentially":[70,106],"under":[72,108],"arbitrary":[73],"switching.":[74],"When":[75],"not":[76],"same":[83],"Lyapunov-like":[96],"dwell":[110],"time":[111],"scheme.":[112],"Two":[113],"numerical":[114],"examples":[115],"provided":[117],"to":[118],"demonstrate":[119],"result.":[121]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
