{"id":"https://openalex.org/W2076444099","doi":"https://doi.org/10.1137/040612531","title":"The Geometry of the Reachability Set for Linear Discrete-time Systems with Positive Controls","display_name":"The Geometry of the Reachability Set for Linear Discrete-time Systems with Positive Controls","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W2076444099","doi":"https://doi.org/10.1137/040612531","mag":"2076444099"},"language":"en","primary_location":{"is_oa":false,"landing_page_url":"https://doi.org/10.1137/040612531","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"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":null,"is_accepted":false,"is_published":false},"type":"article","type_crossref":"journal-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/A5076225221","display_name":"Luca Benvenuti","orcid":"https://orcid.org/0000-0001-7424-6853"},"institutions":[{"id":"https://openalex.org/I861853513","display_name":"Sapienza University of Rome","ror":"https://ror.org/02be6w209","country_code":"IT","type":"education","lineage":["https://openalex.org/I861853513"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Luca Benvenuti","raw_affiliation_strings":["Sapienza, university of Rome"],"affiliations":[{"raw_affiliation_string":"Sapienza, university of Rome","institution_ids":["https://openalex.org/I861853513"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5074179530","display_name":"Lorenzo Farina","orcid":"https://orcid.org/0000-0001-8314-6029"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lorenzo Farina","raw_affiliation_strings":[],"affiliations":[]}],"institution_assertions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"fulltext_origin":"ngrams","cited_by_count":17,"citation_normalized_percentile":{"value":0.929236,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":85,"max":86},"biblio":{"volume":"28","issue":"2","first_page":"306","last_page":"325"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.9995,"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":0.9995,"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/T10791","display_name":"Advanced Control Systems Optimization","score":0.9983,"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/T10142","display_name":"Formal Methods in Verification","score":0.9912,"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/cone","display_name":"Cone (formal languages)","score":0.58325154},{"id":"https://openalex.org/keywords/invariant-subspace","display_name":"Invariant subspace","score":0.4870737}],"concepts":[{"id":"https://openalex.org/C136643341","wikidata":"https://www.wikidata.org/wiki/Q1361526","display_name":"Reachability","level":2,"score":0.8592848},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.84756505},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.64398307},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.61654806},{"id":"https://openalex.org/C30014739","wikidata":"https://www.wikidata.org/wiki/Q5159445","display_name":"Cone (formal languages)","level":2,"score":0.58325154},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.55745316},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.55714},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5270674},{"id":"https://openalex.org/C2777059694","wikidata":"https://www.wikidata.org/wiki/Q2706744","display_name":"Invariant subspace","level":3,"score":0.4870737},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.436167},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.43567783},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3231302},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32291746},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.27551848},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.25974423},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.20601988},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.087999195},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"is_oa":false,"landing_page_url":"https://doi.org/10.1137/040612531","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"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":null,"is_accepted":false,"is_published":false}],"best_oa_location":null,"sustainable_development_goals":[],"grants":[],"datasets":[],"versions":[],"referenced_works_count":17,"referenced_works":["https://openalex.org/W1500921805","https://openalex.org/W1968010891","https://openalex.org/W1968461884","https://openalex.org/W1972435218","https://openalex.org/W1982798315","https://openalex.org/W1989030530","https://openalex.org/W1991579213","https://openalex.org/W2031917840","https://openalex.org/W2055629738","https://openalex.org/W2095226528","https://openalex.org/W2101037112","https://openalex.org/W2170716649","https://openalex.org/W2610857016","https://openalex.org/W391578156","https://openalex.org/W4249667877","https://openalex.org/W4250054333","https://openalex.org/W76640975"],"related_works":["https://openalex.org/W4287164812","https://openalex.org/W4285605394","https://openalex.org/W3213150849","https://openalex.org/W3172436493","https://openalex.org/W3100286349","https://openalex.org/W2957492749","https://openalex.org/W2896134808","https://openalex.org/W2386063599","https://openalex.org/W1975884855","https://openalex.org/W1887135636"],"abstract_inverted_index":{"In":[0,49],"this":[1],"paper":[2],"we":[3,61],"study":[4],"the":[5,9,38,58,67,70,82],"geometrical":[6,55],"properties":[7],"of":[8,11,14,41,57,69,81,87],"set":[10,28],"reachable":[12,59,72],"states":[13],"a":[15,30,42,46,53,63],"single":[16],"input":[17],"discrete-time":[18],"linear":[19,43],"time":[20],"invariant":[21],"(LTI)":[22],"system":[23],"with":[24],"positive":[25],"controls.":[26],"This":[27],"is":[29],"cone":[31,84],"and":[32,45,74,76],"it":[33],"can":[34],"be":[35],"expressed":[36],"as":[37],"direct":[39],"sum":[40],"subspace":[44,73],"proper":[47,83],"cone.":[48],"order":[50],"to":[51,65],"give":[52],"complete":[54],"characterization":[56],"set,":[60],"provide":[62],"formula":[64],"evaluate":[66],"dimension":[68],"largest":[71],"necessary":[75],"sufficient":[77],"conditions":[78],"for":[79],"polyhedrality":[80],"in":[85],"terms":[86],"eigenvalues":[88],"location.":[89]},"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W2076444099","counts_by_year":[{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2025-01-05T22:41:23.996901","created_date":"2016-06-24"}