{"id":"https://openalex.org/W2042024445","doi":"https://doi.org/10.1137/070679740","title":"On Stability and Robust Stability of Positive Linear Volterra Equations","display_name":"On Stability and Robust Stability of Positive Linear Volterra Equations","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W2042024445","doi":"https://doi.org/10.1137/070679740","mag":"2042024445"},"language":"en","primary_location":{"id":"doi:10.1137/070679740","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070679740","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"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":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","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/A5050956546","display_name":"Pham Huu Anh Ngoc","orcid":"https://orcid.org/0000-0002-7958-9254"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Pham Huu Anh Ngoc","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109206355","display_name":"Toshiki Naito","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Toshiki Naito","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101659246","display_name":"Jong Son Shin","orcid":"https://orcid.org/0000-0002-2602-6837"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jong Son Shin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5018341927","display_name":"Satoru Murakami","orcid":"https://orcid.org/0000-0001-9601-2601"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Satoru Murakami","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.1952,"has_fulltext":false,"cited_by_count":34,"citation_normalized_percentile":{"value":0.95779987,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"47","issue":"2","first_page":"975","last_page":"996"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9986000061035156,"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":0.9984999895095825,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8824663162231445},{"id":"https://openalex.org/keywords/volterra-equations","display_name":"Volterra equations","score":0.6698888540267944},{"id":"https://openalex.org/keywords/volterra-integral-equation","display_name":"Volterra integral equation","score":0.6530089378356934},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.6446839570999146},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.6061239838600159},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4591154456138611},{"id":"https://openalex.org/keywords/linear-equation","display_name":"Linear equation","score":0.45579394698143005},{"id":"https://openalex.org/keywords/exponential-stability","display_name":"Exponential stability","score":0.44780033826828003},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4436870515346527},{"id":"https://openalex.org/keywords/independent-equation","display_name":"Independent equation","score":0.4233064651489258},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.38618162274360657},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.30366402864456177},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2455795705318451},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.20451778173446655}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8824663162231445},{"id":"https://openalex.org/C2983756050","wikidata":"https://www.wikidata.org/wiki/Q150052","display_name":"Volterra equations","level":3,"score":0.6698888540267944},{"id":"https://openalex.org/C21965488","wikidata":"https://www.wikidata.org/wiki/Q2632613","display_name":"Volterra integral equation","level":3,"score":0.6530089378356934},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.6446839570999146},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.6061239838600159},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4591154456138611},{"id":"https://openalex.org/C77346573","wikidata":"https://www.wikidata.org/wiki/Q484637","display_name":"Linear equation","level":2,"score":0.45579394698143005},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.44780033826828003},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4436870515346527},{"id":"https://openalex.org/C200602138","wikidata":"https://www.wikidata.org/wiki/Q16979193","display_name":"Independent equation","level":3,"score":0.4233064651489258},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.38618162274360657},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.30366402864456177},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2455795705318451},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.20451778173446655},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/070679740","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070679740","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"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":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":43,"referenced_works":["https://openalex.org/W22103694","https://openalex.org/W210876736","https://openalex.org/W624020015","https://openalex.org/W627859210","https://openalex.org/W804452486","https://openalex.org/W1521302685","https://openalex.org/W1527296550","https://openalex.org/W1534430411","https://openalex.org/W1579645751","https://openalex.org/W1589081551","https://openalex.org/W1594563152","https://openalex.org/W1605729676","https://openalex.org/W1608548244","https://openalex.org/W1971910019","https://openalex.org/W1976873692","https://openalex.org/W1980256444","https://openalex.org/W1981501421","https://openalex.org/W1983868185","https://openalex.org/W2007388965","https://openalex.org/W2010004902","https://openalex.org/W2014456757","https://openalex.org/W2020322142","https://openalex.org/W2032991116","https://openalex.org/W2042105930","https://openalex.org/W2047790746","https://openalex.org/W2050649877","https://openalex.org/W2062448723","https://openalex.org/W2065259455","https://openalex.org/W2071376769","https://openalex.org/W2073540225","https://openalex.org/W2074412622","https://openalex.org/W2075076696","https://openalex.org/W2081921309","https://openalex.org/W2084211207","https://openalex.org/W2088985692","https://openalex.org/W2093410298","https://openalex.org/W2116837988","https://openalex.org/W2127962794","https://openalex.org/W2130813144","https://openalex.org/W2144781470","https://openalex.org/W2163226130","https://openalex.org/W2165716201","https://openalex.org/W2610857016"],"related_works":["https://openalex.org/W2145565532","https://openalex.org/W2021824718","https://openalex.org/W1969626089","https://openalex.org/W4366999453","https://openalex.org/W4307488364","https://openalex.org/W2417357297","https://openalex.org/W224037237","https://openalex.org/W1977785520","https://openalex.org/W334030500","https://openalex.org/W2059178215"],"abstract_inverted_index":{"We":[0],"first":[1],"introduce":[2],"the":[3,89,96],"notion":[4],"of":[5,16,45,53,69,91,95,98],"positive":[6,18,28,46,54,66,70],"linear":[7,29,55,71],"Volterra":[8,30,56,72],"integrodifferential":[9,31,57],"equations.":[10,19,47,58],"Then":[11,35],"we":[12,36,49],"give":[13],"some":[14],"characterizations":[15],"these":[17],"An":[20],"explicit":[21,86],"criterion":[22,40],"and":[23,65,81],"a":[24,38],"Perron\u2013Frobenius-type":[25],"theorem":[26],"for":[27,41],"equations":[32,73],"are":[33,101],"given.":[34],"offer":[37],"new":[39],"uniformly":[42],"asymptotic":[43],"stability":[44,51,67],"Finally,":[48],"study":[50],"radii":[52,68],"It":[59],"is":[60],"proved":[61],"that":[62],"complex,":[63],"real,":[64],"under":[74],"structured":[75],"perturbations":[76],"(or":[77],"affine":[78],"perturbations)":[79],"coincide":[80],"can":[82],"be":[83],"computed":[84],"by":[85],"formulae.":[87],"To":[88],"best":[90],"our":[92],"knowledge,":[93],"most":[94],"results":[97],"this":[99],"paper":[100],"new.":[102]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":3}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
