{"id":"https://openalex.org/W2075606892","doi":"https://doi.org/10.1109/cdc.2013.6759965","title":"Polytope joint Lyapunov functions for positive LSS","display_name":"Polytope joint Lyapunov functions for positive LSS","publication_year":2013,"publication_date":"2013-12-01","ids":{"openalex":"https://openalex.org/W2075606892","doi":"https://doi.org/10.1109/cdc.2013.6759965","mag":"2075606892"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2013.6759965","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2013.6759965","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"52nd IEEE Conference on Decision and Control","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/A5030219464","display_name":"Nicola Guglielmi","orcid":"https://orcid.org/0000-0003-3795-5225"},"institutions":[{"id":"https://openalex.org/I26415053","display_name":"University of L'Aquila","ror":"https://ror.org/01j9p1r26","country_code":"IT","type":"education","lineage":["https://openalex.org/I26415053"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Nicola Guglielmi","raw_affiliation_strings":["Dipartimento di Ingegneria, Scienze Informatiche e Matematica, University of L\u2019 Aquila, L'Aquila, Italy","Dipt. di Ing., Sci. Informatiche e Mat., Univ. of L'Aquila, L'Aquila, Italy"],"affiliations":[{"raw_affiliation_string":"Dipartimento di Ingegneria, Scienze Informatiche e Matematica, University of L\u2019 Aquila, L'Aquila, Italy","institution_ids":["https://openalex.org/I26415053"]},{"raw_affiliation_string":"Dipt. di Ing., Sci. Informatiche e Mat., Univ. of L'Aquila, L'Aquila, Italy","institution_ids":["https://openalex.org/I26415053"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5014455027","display_name":"Linda Laglia","orcid":null},"institutions":[{"id":"https://openalex.org/I26415053","display_name":"University of L'Aquila","ror":"https://ror.org/01j9p1r26","country_code":"IT","type":"education","lineage":["https://openalex.org/I26415053"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Linda Laglia","raw_affiliation_strings":["Dipartimento di Ingegneria, Scienze Informatiche e Matematica, University of L\u2019 Aquila, L'Aquila, Italy","Dipt. di Ing., Sci. Informatiche e Mat., Univ. of L'Aquila, L'Aquila, Italy"],"affiliations":[{"raw_affiliation_string":"Dipartimento di Ingegneria, Scienze Informatiche e Matematica, University of L\u2019 Aquila, L'Aquila, Italy","institution_ids":["https://openalex.org/I26415053"]},{"raw_affiliation_string":"Dipt. di Ing., Sci. Informatiche e Mat., Univ. of L'Aquila, L'Aquila, Italy","institution_ids":["https://openalex.org/I26415053"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5030219464"],"corresponding_institution_ids":["https://openalex.org/I26415053"],"apc_list":null,"apc_paid":null,"fwci":1.0099,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.81325424,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"425","issue":null,"first_page":"710","last_page":"715"},"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9987000226974487,"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"}},{"id":"https://openalex.org/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.9952999949455261,"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/polytope","display_name":"Polytope","score":0.8161413669586182},{"id":"https://openalex.org/keywords/lyapunov-exponent","display_name":"Lyapunov exponent","score":0.7265116572380066},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.649172306060791},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.5952531695365906},{"id":"https://openalex.org/keywords/orthant","display_name":"Orthant","score":0.5371478199958801},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.4920589327812195},{"id":"https://openalex.org/keywords/lyapunov-equation","display_name":"Lyapunov equation","score":0.46875858306884766},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4603421986103058},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.42006564140319824},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.36648833751678467},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.26779863238334656},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1231573224067688},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.0842566192150116}],"concepts":[{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.8161413669586182},{"id":"https://openalex.org/C191544260","wikidata":"https://www.wikidata.org/wiki/Q1238630","display_name":"Lyapunov exponent","level":3,"score":0.7265116572380066},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.649172306060791},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.5952531695365906},{"id":"https://openalex.org/C2780016784","wikidata":"https://www.wikidata.org/wiki/Q2714507","display_name":"Orthant","level":2,"score":0.5371478199958801},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.4920589327812195},{"id":"https://openalex.org/C25854792","wikidata":"https://www.wikidata.org/wiki/Q1028945","display_name":"Lyapunov equation","level":4,"score":0.46875858306884766},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4603421986103058},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.42006564140319824},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.36648833751678467},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.26779863238334656},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1231573224067688},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.0842566192150116},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"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/cdc.2013.6759965","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2013.6759965","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"52nd IEEE Conference on Decision and Control","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W1534430411","https://openalex.org/W1547943045","https://openalex.org/W1642990561","https://openalex.org/W1880805667","https://openalex.org/W1971453285","https://openalex.org/W1971934985","https://openalex.org/W1987769823","https://openalex.org/W1988610190","https://openalex.org/W1999878649","https://openalex.org/W2020979852","https://openalex.org/W2032326995","https://openalex.org/W2036612299","https://openalex.org/W2040235632","https://openalex.org/W2060886109","https://openalex.org/W2068617307","https://openalex.org/W2076566814","https://openalex.org/W2096474812","https://openalex.org/W2103966928","https://openalex.org/W2120207446","https://openalex.org/W2131370775","https://openalex.org/W2144098960","https://openalex.org/W2963431627","https://openalex.org/W4235143360","https://openalex.org/W4238257903","https://openalex.org/W6766247529"],"related_works":["https://openalex.org/W4299806624","https://openalex.org/W2781909303","https://openalex.org/W2962947512","https://openalex.org/W2228501551","https://openalex.org/W2284157877","https://openalex.org/W1983507234","https://openalex.org/W2349796700","https://openalex.org/W2383986032","https://openalex.org/W2030955003","https://openalex.org/W1979419366"],"abstract_inverted_index":{"We":[0],"consider":[1],"switched":[2],"linear":[3],"systems":[4,83],"of":[5,17,30,39,53,74,81,93,155,165],"odes,":[6],"\u1e8b":[7],"x(t)=":[8],"A(u(t))x(t)":[9],"where":[10,99],"A(u(t))":[11],"\u2208":[12],"A,":[13],"a":[14,24,79,118,140],"compact":[15],"set":[16],"matrices.":[18],"In":[19],"this":[20,156],"paper":[21],"we":[22,142],"propose":[23],"new":[25],"method":[26,67],"for":[27,55,78,135],"the":[28,31,40,43,51,71,87,125,136,145],"approximation":[29],"upper":[32,131],"Lyapunov":[33,37,122,137],"exponent":[34,38],"and":[35,132],"lower":[36,133],"LSS":[41],"when":[42],"matrices":[44,49],"in":[45,59,160],"A":[46],"are":[47,113],"Metzler":[48],"(or":[50],"generalization":[52],"them":[54],"arbitrary":[56],"cone),":[57],"arising":[58],"many":[60],"interesting":[61],"applications":[62],"(see":[63],"e.g.":[64],"[9]).":[65],"The":[66,153],"is":[68,148,158],"based":[69],"on":[70,124],"iterative":[72],"construction":[73],"invariant":[75],"positive":[76,126],"polytopes":[77,112],"sequence":[80],"discretized":[82],"obtained":[84],"by":[85],"forcing":[86],"switching":[88],"instants":[89],"to":[90,116],"be":[91],"multiple":[92],"\u0394":[94,100],"<sup":[95,101],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[96,102],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">(k)</sup>":[97,103],"t":[98,104],"\u2192":[105,109],"0":[106],"as":[107],"k":[108],"\u221e.":[110],"These":[111],"then":[114],"used":[115],"generate":[117],"monotone":[119],"piecewise-linear":[120],"joint":[121],"function":[123],"orthant,":[127],"which":[128],"gives":[129],"tight":[130],"bounds":[134],"exponents.":[138],"As":[139],"byproduct":[141],"detect":[143],"whether":[144],"considered":[146],"system":[147],"stabilizable":[149],"or":[150],"uniformly":[151],"stable.":[152],"efficiency":[154],"approach":[157],"demonstrated":[159],"numerical":[161],"examples,":[162],"including":[163],"some":[164],"relatively":[166],"large":[167],"dimensions.":[168]},"counts_by_year":[{"year":2015,"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"}
