{"id":"https://openalex.org/W2028881181","doi":"https://doi.org/10.1080/00207720903480691","title":"Reachability analysis of rational eigenvalue linear systems","display_name":"Reachability analysis of rational eigenvalue linear systems","publication_year":2010,"publication_date":"2010-10-21","ids":{"openalex":"https://openalex.org/W2028881181","doi":"https://doi.org/10.1080/00207720903480691","mag":"2028881181"},"language":"en","primary_location":{"id":"doi:10.1080/00207720903480691","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207720903480691","pdf_url":null,"source":{"id":"https://openalex.org/S129640837","display_name":"International Journal of Systems Science","issn_l":"0020-7721","issn":["0020-7721","1464-5319"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Systems Science","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/A5060776618","display_name":"Ming Xu","orcid":"https://orcid.org/0000-0002-9906-5677"},"institutions":[{"id":"https://openalex.org/I66867065","display_name":"East China Normal University","ror":"https://ror.org/02n96ep67","country_code":"CN","type":"education","lineage":["https://openalex.org/I66867065"]},{"id":"https://openalex.org/I4210139618","display_name":"Shanghai Key Laboratory of Trustworthy Computing","ror":"https://ror.org/030qbr085","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210139618"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ming Xu","raw_affiliation_strings":["\n Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai 200062, China;\n Computer Science and Technology Department, East China Normal University, Shanghai 200241, China","Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai 200062, China","Computer Science and Technology Department, East China Normal University, Shanghai 200241, China"],"affiliations":[{"raw_affiliation_string":"\n Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai 200062, China;\n Computer Science and Technology Department, East China Normal University, Shanghai 200241, China","institution_ids":["https://openalex.org/I4210139618","https://openalex.org/I66867065"]},{"raw_affiliation_string":"Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai 200062, China","institution_ids":["https://openalex.org/I4210139618","https://openalex.org/I66867065"]},{"raw_affiliation_string":"Computer Science and Technology Department, East China Normal University, Shanghai 200241, China","institution_ids":["https://openalex.org/I66867065"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100780219","display_name":"Liangyu Chen","orcid":"https://orcid.org/0000-0003-0394-6208"},"institutions":[{"id":"https://openalex.org/I4210139618","display_name":"Shanghai Key Laboratory of Trustworthy Computing","ror":"https://ror.org/030qbr085","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210139618"]},{"id":"https://openalex.org/I66867065","display_name":"East China Normal University","ror":"https://ror.org/02n96ep67","country_code":"CN","type":"education","lineage":["https://openalex.org/I66867065"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Liangyu Chen","raw_affiliation_strings":["\n Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai 200062, China","Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai 200062, China"],"affiliations":[{"raw_affiliation_string":"\n Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai 200062, China","institution_ids":["https://openalex.org/I4210139618"]},{"raw_affiliation_string":"Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai 200062, China","institution_ids":["https://openalex.org/I4210139618","https://openalex.org/I66867065"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058328411","display_name":"Zhenbing Zeng","orcid":"https://orcid.org/0000-0002-9728-1114"},"institutions":[{"id":"https://openalex.org/I4210139618","display_name":"Shanghai Key Laboratory of Trustworthy Computing","ror":"https://ror.org/030qbr085","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210139618"]},{"id":"https://openalex.org/I66867065","display_name":"East China Normal University","ror":"https://ror.org/02n96ep67","country_code":"CN","type":"education","lineage":["https://openalex.org/I66867065"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhenbing Zeng","raw_affiliation_strings":["\n Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai 200062, China","Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai 200062, China"],"affiliations":[{"raw_affiliation_string":"\n Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai 200062, China","institution_ids":["https://openalex.org/I4210139618"]},{"raw_affiliation_string":"Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai 200062, China","institution_ids":["https://openalex.org/I4210139618","https://openalex.org/I66867065"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100351560","display_name":"Zhibin Li","orcid":"https://orcid.org/0000-0002-6357-7419"},"institutions":[{"id":"https://openalex.org/I4210139618","display_name":"Shanghai Key Laboratory of Trustworthy Computing","ror":"https://ror.org/030qbr085","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210139618"]},{"id":"https://openalex.org/I66867065","display_name":"East China Normal University","ror":"https://ror.org/02n96ep67","country_code":"CN","type":"education","lineage":["https://openalex.org/I66867065"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Zhi-bin Li","raw_affiliation_strings":["\n Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai 200062, China;\n Computer Science and Technology Department, East China Normal University, Shanghai 200241, China","Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai 200062, China","Computer Science and Technology Department, East China Normal University, Shanghai 200241, China"],"affiliations":[{"raw_affiliation_string":"\n Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai 200062, China;\n Computer Science and Technology Department, East China Normal University, Shanghai 200241, China","institution_ids":["https://openalex.org/I4210139618","https://openalex.org/I66867065"]},{"raw_affiliation_string":"Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai 200062, China","institution_ids":["https://openalex.org/I4210139618","https://openalex.org/I66867065"]},{"raw_affiliation_string":"Computer Science and Technology Department, East China Normal University, Shanghai 200241, China","institution_ids":["https://openalex.org/I66867065"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5100351560"],"corresponding_institution_ids":["https://openalex.org/I4210139618","https://openalex.org/I66867065"],"apc_list":null,"apc_paid":null,"fwci":2.3417,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.87996439,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"41","issue":"12","first_page":"1411","last_page":"1419"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.9994999766349792,"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"}},"topics":[{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.9994999766349792,"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/T10791","display_name":"Advanced Control Systems Optimization","score":0.9919000267982483,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9832000136375427,"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/reachability","display_name":"Reachability","score":0.9000867605209351},{"id":"https://openalex.org/keywords/observability","display_name":"Observability","score":0.6434244513511658},{"id":"https://openalex.org/keywords/controllability","display_name":"Controllability","score":0.6420121788978577},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.6336959004402161},{"id":"https://openalex.org/keywords/decidability","display_name":"Decidability","score":0.607598602771759},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4570823013782501},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.44634127616882324},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.4304613471031189},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4106175899505615},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3943966031074524},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.34858623147010803},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.32138118147850037},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3108753561973572},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.24009919166564941},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2034812867641449}],"concepts":[{"id":"https://openalex.org/C136643341","wikidata":"https://www.wikidata.org/wiki/Q1361526","display_name":"Reachability","level":2,"score":0.9000867605209351},{"id":"https://openalex.org/C36299963","wikidata":"https://www.wikidata.org/wiki/Q1369844","display_name":"Observability","level":2,"score":0.6434244513511658},{"id":"https://openalex.org/C48209547","wikidata":"https://www.wikidata.org/wiki/Q1331104","display_name":"Controllability","level":2,"score":0.6420121788978577},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.6336959004402161},{"id":"https://openalex.org/C153269930","wikidata":"https://www.wikidata.org/wiki/Q430001","display_name":"Decidability","level":2,"score":0.607598602771759},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4570823013782501},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.44634127616882324},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.4304613471031189},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4106175899505615},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3943966031074524},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.34858623147010803},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.32138118147850037},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3108753561973572},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.24009919166564941},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2034812867641449},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207720903480691","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207720903480691","pdf_url":null,"source":{"id":"https://openalex.org/S129640837","display_name":"International Journal of Systems Science","issn_l":"0020-7721","issn":["0020-7721","1464-5319"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Systems Science","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322370","display_name":"East China Normal University","ror":"https://ror.org/02n96ep67"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W130102441","https://openalex.org/W1498285565","https://openalex.org/W1553142094","https://openalex.org/W1569146343","https://openalex.org/W1582811927","https://openalex.org/W1726255445","https://openalex.org/W1868193499","https://openalex.org/W1878064217","https://openalex.org/W1970473241","https://openalex.org/W1994475353","https://openalex.org/W2000840790","https://openalex.org/W2001950210","https://openalex.org/W2002571332","https://openalex.org/W2004417356","https://openalex.org/W2004463571","https://openalex.org/W2007074311","https://openalex.org/W2055960145","https://openalex.org/W2076597612","https://openalex.org/W2085838366","https://openalex.org/W2093964259","https://openalex.org/W2126749600","https://openalex.org/W2155321341","https://openalex.org/W2162269500","https://openalex.org/W3159477971","https://openalex.org/W3175367423","https://openalex.org/W3217399827","https://openalex.org/W4229917934","https://openalex.org/W4243409352","https://openalex.org/W4245682190","https://openalex.org/W4247561795","https://openalex.org/W4298290503"],"related_works":["https://openalex.org/W1986570998","https://openalex.org/W2332386680","https://openalex.org/W1983142522","https://openalex.org/W2782529250","https://openalex.org/W2037921533","https://openalex.org/W2801563517","https://openalex.org/W2130864543","https://openalex.org/W2508171592","https://openalex.org/W2068126039","https://openalex.org/W2153544183"],"abstract_inverted_index":{"Abstract":[0],"One":[1],"of":[2,10,17,31,60,80,149,166],"the":[3,7,14,27,73,144,161],"key":[4],"problems":[5],"in":[6,36,89],"safety":[8],"analysis":[9,75],"control":[11],"systems":[12,33,37,62],"is":[13,69,140],"exact":[15],"computation":[16,96],"reachable":[18,65],"state":[19,66],"spaces":[20],"for":[21,48,129],"continuous-time":[22],"systems.":[23,51],"Issues":[24],"related":[25],"to":[26,76,99],"controllability":[28],"and":[29,97,125,132,160],"observability":[30],"these":[32],"are":[34,41],"well-studied":[35],"theory.":[38],"However,":[39],"there":[40],"not":[42],"many":[43],"results":[44],"on":[45,94,135],"reachability,":[46],"even":[47],"general":[49],"linear":[50,61],"In":[52],"this":[53,87],"study,":[54],"we":[55,84],"present":[56],"a":[57,90],"large":[58],"class":[59],"with":[63],"decidable":[64],"spaces.":[67],"This":[68,138],"approached":[70],"by":[71,143],"reducing":[72],"reachability":[74,104],"real":[77],"root":[78,107],"isolation":[79],"exponential":[81],"polynomials.":[82],"Furthermore,":[83],"have":[85],"implemented":[86],"method":[88],"Maple":[91],"package":[92],"based":[93],"symbolic":[95],"applied":[98],"several":[100],"examples":[101],"successfully.":[102],"Keywords:":[103],"analysislinear":[105],"systemsreal":[106],"isolationexponential":[108],"polynomialscontinued":[109],"fractionsinterval":[110],"arithmetic":[111],"Acknowledgements":[112],"We":[113],"gratefully":[114],"thank":[115],"Prof.":[116,119],"Lu":[117],"Yang,":[118],"Wensheng":[120],"Yu,":[121],"Dr":[122,126],"Min":[123],"Wu":[124],"Zhengfeng":[127],"Yang":[128],"their":[130],"beneficial":[131],"helpful":[133],"comments":[134],"our":[136],"work.":[137],"work":[139],"partially":[141],"supported":[142],"National":[145],"Natural":[146],"Science":[147],"Foundation":[148],"China":[150],"(No.":[151,158,169],"90718041),":[152],"Shanghai":[153],"Leading":[154],"Academic":[155],"Discipline":[156],"Project":[157],"B412)":[159],"PhD":[162],"Programme":[163],"Scholarship":[164],"Fund":[165],"ECNU":[167],"2009":[168],"2009056).":[170]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
