{"id":"https://openalex.org/W2981844804","doi":"https://doi.org/10.3390/e21111045","title":"On the Approximated Reachability of a Class of Time-Varying Nonlinear Dynamic Systems Based on Their Linearized Behavior about the Equilibria: Applications to Epidemic Models","display_name":"On the Approximated Reachability of a Class of Time-Varying Nonlinear Dynamic Systems Based on Their Linearized Behavior about the Equilibria: Applications to Epidemic Models","publication_year":2019,"publication_date":"2019-10-26","ids":{"openalex":"https://openalex.org/W2981844804","doi":"https://doi.org/10.3390/e21111045","mag":"2981844804"},"language":"en","primary_location":{"id":"doi:10.3390/e21111045","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e21111045","pdf_url":"https://www.mdpi.com/1099-4300/21/11/1045/pdf?version=1573209575","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/21/11/1045/pdf?version=1573209575","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5042326806","display_name":"Manuel De la Sen","orcid":"https://orcid.org/0000-0001-9320-9433"},"institutions":[{"id":"https://openalex.org/I169108374","display_name":"University of the Basque Country","ror":"https://ror.org/000xsnr85","country_code":"ES","type":"education","lineage":["https://openalex.org/I169108374"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Manuel De la Sen","raw_affiliation_strings":["Institute of Research and Development of Processes IIDP, University of the Basque Country, Campus of Leioa, P.O. Box 48940, Leioa, 48940 Bizkaia, Spain"],"raw_orcid":"https://orcid.org/0000-0001-9320-9433","affiliations":[{"raw_affiliation_string":"Institute of Research and Development of Processes IIDP, University of the Basque Country, Campus of Leioa, P.O. Box 48940, Leioa, 48940 Bizkaia, Spain","institution_ids":["https://openalex.org/I169108374"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5042326806"],"corresponding_institution_ids":["https://openalex.org/I169108374"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.3404,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.57698816,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"21","issue":"11","first_page":"1045","last_page":"1045"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10410","display_name":"COVID-19 epidemiological studies","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10410","display_name":"COVID-19 epidemiological studies","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9962999820709229,"subfield":{"id":"https://openalex.org/subfields/2739","display_name":"Public Health, Environmental and Occupational Health"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T10621","display_name":"Gene Regulatory Network Analysis","score":0.9039999842643738,"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/controllability","display_name":"Controllability","score":0.8068719506263733},{"id":"https://openalex.org/keywords/reachability","display_name":"Reachability","score":0.7965118885040283},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.7303948402404785},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6923306584358215},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5677840113639832},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.549898624420166},{"id":"https://openalex.org/keywords/controllability-gramian","display_name":"Controllability Gramian","score":0.48720043897628784},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.4790676534175873},{"id":"https://openalex.org/keywords/lti-system-theory","display_name":"LTI system theory","score":0.45654770731925964},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4498051702976227},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2895601987838745},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.20378810167312622},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.10662513971328735},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06961923837661743}],"concepts":[{"id":"https://openalex.org/C48209547","wikidata":"https://www.wikidata.org/wiki/Q1331104","display_name":"Controllability","level":2,"score":0.8068719506263733},{"id":"https://openalex.org/C136643341","wikidata":"https://www.wikidata.org/wiki/Q1361526","display_name":"Reachability","level":2,"score":0.7965118885040283},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.7303948402404785},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6923306584358215},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5677840113639832},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.549898624420166},{"id":"https://openalex.org/C143461762","wikidata":"https://www.wikidata.org/wiki/Q83587","display_name":"Controllability Gramian","level":3,"score":0.48720043897628784},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.4790676534175873},{"id":"https://openalex.org/C87698059","wikidata":"https://www.wikidata.org/wiki/Q1808960","display_name":"LTI system theory","level":3,"score":0.45654770731925964},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4498051702976227},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2895601987838745},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.20378810167312622},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.10662513971328735},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06961923837661743},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/e21111045","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e21111045","pdf_url":"https://www.mdpi.com/1099-4300/21/11/1045/pdf?version=1573209575","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:413266ab2e9e4269b8fc2d523d4ac829","is_oa":true,"landing_page_url":"https://doaj.org/article/413266ab2e9e4269b8fc2d523d4ac829","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 21, Iss 11, p 1045 (2019)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/21/11/1045/","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/e21111045","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy","raw_type":"Text"},{"id":"pmh:oai:pubmedcentral.nih.gov:7514349","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/7514349","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy (Basel)","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e21111045","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e21111045","pdf_url":"https://www.mdpi.com/1099-4300/21/11/1045/pdf?version=1573209575","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.8199999928474426,"display_name":"Good health and well-being","id":"https://metadata.un.org/sdg/3"}],"awards":[{"id":"https://openalex.org/G3821461479","display_name":null,"funder_award_id":"IT1207-19","funder_id":"https://openalex.org/F4320321705","funder_display_name":"Eusko Jaurlaritza"}],"funders":[{"id":"https://openalex.org/F4320321705","display_name":"Eusko Jaurlaritza","ror":"https://ror.org/00pz2fp31"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W1598438289","https://openalex.org/W1811601109","https://openalex.org/W1979997314","https://openalex.org/W2000354797","https://openalex.org/W2004826528","https://openalex.org/W2030487651","https://openalex.org/W2081017921","https://openalex.org/W2087171258","https://openalex.org/W2333248832","https://openalex.org/W2522820290","https://openalex.org/W2793644083","https://openalex.org/W2803198451","https://openalex.org/W2883934420","https://openalex.org/W2888419958","https://openalex.org/W2924896513","https://openalex.org/W2927659276","https://openalex.org/W2936933032","https://openalex.org/W2940956383","https://openalex.org/W2942096894","https://openalex.org/W2956533078","https://openalex.org/W2966780612","https://openalex.org/W4231605584","https://openalex.org/W6727095926","https://openalex.org/W6761388388"],"related_works":["https://openalex.org/W3209184047","https://openalex.org/W2119819375","https://openalex.org/W2059046304","https://openalex.org/W72451598","https://openalex.org/W1942635442","https://openalex.org/W4237454804","https://openalex.org/W2054831413","https://openalex.org/W1990421243","https://openalex.org/W1556353120","https://openalex.org/W2003019938"],"abstract_inverted_index":{"This":[0],"paper":[1],"formulates":[2],"the":[3,55,64,67,80,90,94,102,106,117,123,139,142,150,153,157,164],"properties":[4],"of":[5,12,54,105,116,156,163],"point":[6,10],"reachability":[7,11],"and":[8,57,87,148],"approximate":[9],"either":[13],"a":[14,21,27,34,47,52],"targeted":[15],"state":[16,56],"or":[17,114],"output":[18],"values":[19],"in":[20],"general":[22],"dynamic":[23],"system":[24,109,120],"which":[25],"possess":[26],"linear":[28,112,125,158],"time-varying":[29,76,124],"dynamics":[30,48,70,82,96],"with":[31,79,110],"respect":[32],"to":[33,129],"given":[35],"reference":[36],"nominal":[37,69,107],"one":[38],"and,":[39],"eventually,":[40],"an":[41],"unknown":[42],"structured":[43],"nonlinear":[44,81,95],"dynamics.":[45],"Such":[46],"is":[49,71,97,145],"upper-bounded":[50],"by":[51],"function":[53],"input.":[58],"The":[59],"results":[60,135,167],"are":[61,83,127,136,160,172],"obtained":[62,137],"for":[63,89,138,149,168],"case":[65,91,140,151],"when":[66,92,141,152],"time-invariant":[68],"perfectly":[72],"known":[73,86],"while":[74],"its":[75],"deviations":[77],"together":[78],"not":[84,98],"precisely":[85,99],"also":[88,173],"only":[93],"known.":[100],"Either":[101],"controllability":[103,154],"gramian":[104],"linearized":[108,119],"constant":[111],"parameterization":[113],"that":[115],"current":[118],"(which":[121],"includes":[122],"dynamics)":[126],"assumed":[128],"be":[130],"non-singular.":[131],"Also,":[132],"some":[133,169],"further":[134],"control":[143],"input":[144],"eventually":[146],"saturated":[147],"gramians":[155],"parts":[159],"singular.":[161],"Examples":[162],"derived":[165],"theoretical":[166],"epidemic":[170],"models":[171],"discussed.":[174]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2019-11-01T00:00:00"}
