{"id":"https://openalex.org/W2096706473","doi":"https://doi.org/10.1109/cdc.2010.5717288","title":"Stability of switched linear systems on cones: A generating function approach","display_name":"Stability of switched linear systems on cones: A generating function approach","publication_year":2010,"publication_date":"2010-12-01","ids":{"openalex":"https://openalex.org/W2096706473","doi":"https://doi.org/10.1109/cdc.2010.5717288","mag":"2096706473"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2010.5717288","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2010.5717288","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"49th IEEE Conference on Decision and Control (CDC)","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://mdsoar.org/bitstreams/dbeeb8bb-6d5c-4a67-8a25-223ecfc63eb3/download","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5013733463","display_name":"Jinglai Shen","orcid":"https://orcid.org/0000-0003-2172-4182"},"institutions":[{"id":"https://openalex.org/I126744593","display_name":"University of Maryland, Baltimore","ror":"https://ror.org/04rq5mt64","country_code":"US","type":"education","lineage":["https://openalex.org/I126744593"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Jinglai Shen","raw_affiliation_strings":["Department of Mathematics and Statistics, University of Maryland, Baltimore, MD, USA","Department of Mathematics and Statistics, University of Maryland, Baltimore County 21250, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Maryland, Baltimore, MD, USA","institution_ids":["https://openalex.org/I126744593"]},{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Maryland, Baltimore County 21250, USA","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5035753295","display_name":"Jianghai Hu","orcid":"https://orcid.org/0000-0002-4250-8852"},"institutions":[{"id":"https://openalex.org/I219193219","display_name":"Purdue University West Lafayette","ror":"https://ror.org/02dqehb95","country_code":"US","type":"education","lineage":["https://openalex.org/I219193219"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jianghai Hu","raw_affiliation_strings":["School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN, USA","School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN 47906, USA#TAB#"],"affiliations":[{"raw_affiliation_string":"School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN, USA","institution_ids":["https://openalex.org/I219193219"]},{"raw_affiliation_string":"School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN 47906, USA#TAB#","institution_ids":["https://openalex.org/I219193219"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5013733463"],"corresponding_institution_ids":["https://openalex.org/I126744593"],"apc_list":null,"apc_paid":null,"fwci":2.1876,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.89626087,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"420","last_page":"425"},"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/T11110","display_name":"Stability and Controllability of Differential Equations","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/T10621","display_name":"Gene Regulatory Network Analysis","score":0.9961000084877014,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/exponential-stability","display_name":"Exponential stability","score":0.7672791481018066},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6393143534660339},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.6156142354011536},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.584670901298523},{"id":"https://openalex.org/keywords/cone","display_name":"Cone (formal languages)","score":0.5678020119667053},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5635477900505066},{"id":"https://openalex.org/keywords/euclidean-space","display_name":"Euclidean space","score":0.5312328934669495},{"id":"https://openalex.org/keywords/positive-systems","display_name":"Positive systems","score":0.5209358930587769},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4926837086677551},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.4707867503166199},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.470554381608963},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4422292709350586},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4413106441497803},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.38229840993881226},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.35983961820602417},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2222786545753479},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.1363934874534607},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11126890778541565},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.07674431800842285},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07307696342468262},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.07273158431053162}],"concepts":[{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.7672791481018066},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6393143534660339},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.6156142354011536},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.584670901298523},{"id":"https://openalex.org/C30014739","wikidata":"https://www.wikidata.org/wiki/Q5159445","display_name":"Cone (formal languages)","level":2,"score":0.5678020119667053},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5635477900505066},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.5312328934669495},{"id":"https://openalex.org/C2778299942","wikidata":"https://www.wikidata.org/wiki/Q7233296","display_name":"Positive systems","level":3,"score":0.5209358930587769},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4926837086677551},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.4707867503166199},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.470554381608963},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4422292709350586},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4413106441497803},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.38229840993881226},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.35983961820602417},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2222786545753479},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.1363934874534607},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11126890778541565},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.07674431800842285},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07307696342468262},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.07273158431053162},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/cdc.2010.5717288","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2010.5717288","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"49th IEEE Conference on Decision and Control (CDC)","raw_type":"proceedings-article"},{"id":"pmh:oai:mdsoar.org:11603/35756","is_oa":true,"landing_page_url":"http://hdl.handle.net/11603/35756","pdf_url":"https://mdsoar.org/bitstreams/dbeeb8bb-6d5c-4a67-8a25-223ecfc63eb3/download","source":{"id":"https://openalex.org/S4306402556","display_name":"Maryland Shared Open Access Repository (USMAI Consortium)","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":null,"raw_type":"Text"},{"id":"doi:10.13016/m2garo-zf7h","is_oa":true,"landing_page_url":"https://doi.org/10.13016/m2garo-zf7h","pdf_url":null,"source":{"id":"https://openalex.org/S4306402644","display_name":"Digital Repository at the University of Maryland (University of Maryland College Park)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I66946132","host_organization_name":"University of Maryland, College Park","host_organization_lineage":["https://openalex.org/I66946132"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"pmh:oai:mdsoar.org:11603/35756","is_oa":true,"landing_page_url":"http://hdl.handle.net/11603/35756","pdf_url":"https://mdsoar.org/bitstreams/dbeeb8bb-6d5c-4a67-8a25-223ecfc63eb3/download","source":{"id":"https://openalex.org/S4306402556","display_name":"Maryland Shared Open Access Repository (USMAI Consortium)","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":null,"raw_type":"Text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5970944286","display_name":"CAREER: Reachability Analysis and Optimization of Stochastic Hybrid Systems","funder_award_id":"0643805","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7984144053","display_name":"Switching Dynamics and Control of Complementarity Systems: a Hybrid System Perspective","funder_award_id":"0900960","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G848032724","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320309204","display_name":"University of Maryland, Baltimore County","ror":"https://ror.org/02qskvh78"},{"id":"https://openalex.org/F4320337392","display_name":"Division of Electrical, Communications and Cyber Systems","ror":"https://ror.org/01krpsy48"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2096706473.pdf","grobid_xml":"https://content.openalex.org/works/W2096706473.grobid-xml"},"referenced_works_count":19,"referenced_works":["https://openalex.org/W1534430411","https://openalex.org/W1552094772","https://openalex.org/W1976209547","https://openalex.org/W1991704703","https://openalex.org/W2028739770","https://openalex.org/W2062974796","https://openalex.org/W2075546205","https://openalex.org/W2084970142","https://openalex.org/W2102022534","https://openalex.org/W2126825123","https://openalex.org/W2142219971","https://openalex.org/W2154510168","https://openalex.org/W2163816227","https://openalex.org/W2169080175","https://openalex.org/W2296319761","https://openalex.org/W4235143360","https://openalex.org/W4250589301","https://openalex.org/W6648249563","https://openalex.org/W6684232431"],"related_works":["https://openalex.org/W2185573112","https://openalex.org/W3203676140","https://openalex.org/W1965191890","https://openalex.org/W172361930","https://openalex.org/W2142388326","https://openalex.org/W2169744002","https://openalex.org/W1996493114","https://openalex.org/W3103466487","https://openalex.org/W2904267548","https://openalex.org/W1484417697"],"abstract_inverted_index":{"This":[0],"paper":[1],"extends":[2],"the":[3,7,19,29,107],"recent":[4],"study":[5],"of":[6,14,28,32,96,106,109,111],"generating":[8,77,113],"function":[9],"approach":[10],"to":[11,22],"stability":[12,52,68,95],"analysis":[13],"switched":[15,33,36,97],"linear":[16,98],"systems":[17,34,38,45,99],"from":[18],"Euclidean":[20],"space":[21],"a":[23],"closed":[24],"convex":[25],"cone.":[26],"Examples":[27],"latter":[30],"class":[31],"include":[35],"positive":[37,47],"that":[39,64],"model":[40],"various":[41],"biologic":[42],"and":[43,50,66,75,83,89],"economic":[44],"with":[46],"states.":[48],"Strong":[49,74],"weak":[51,76],"notions":[53],"are":[54,69,81,86,102],"considered":[55],"in":[56,104],"this":[57],"paper.":[58],"In":[59],"particular,":[60],"it":[61],"is":[62],"shown":[63],"asymptotic":[65],"exponential":[67,94],"equivalent":[70],"for":[71,92],"both":[72],"notions.":[73],"functions":[78],"on":[79,100],"cones":[80,101],"introduced":[82],"their":[84],"properties":[85],"established.":[87],"Necessary":[88],"sufficient":[90],"conditions":[91],"strong/weak":[93,112],"obtained":[103],"terms":[105],"radii":[108],"convergence":[110],"functions.":[114]},"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-03-18T14:38:29.013473","created_date":"2025-10-10T00:00:00"}