{"id":"https://openalex.org/W2057040947","doi":"https://doi.org/10.1093/imamci/dnu030","title":"Output-based stabilization for a one-dimensional wave equation with distributed input delay in the boundary control","display_name":"Output-based stabilization for a one-dimensional wave equation with distributed input delay in the boundary control","publication_year":2014,"publication_date":"2014-07-10","ids":{"openalex":"https://openalex.org/W2057040947","doi":"https://doi.org/10.1093/imamci/dnu030","mag":"2057040947"},"language":"en","primary_location":{"id":"doi:10.1093/imamci/dnu030","is_oa":false,"landing_page_url":"https://doi.org/10.1093/imamci/dnu030","pdf_url":null,"source":{"id":"https://openalex.org/S162756791","display_name":"IMA Journal of Mathematical Control and Information","issn_l":"0265-0754","issn":["0265-0754","1471-6887"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IMA Journal of Mathematical Control and Information","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/A5024753578","display_name":"Ying Shang","orcid":"https://orcid.org/0000-0001-6655-2877"},"institutions":[{"id":"https://openalex.org/I162868743","display_name":"Tianjin University","ror":"https://ror.org/012tb2g32","country_code":"CN","type":"education","lineage":["https://openalex.org/I162868743"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Ying Feng Shang","raw_affiliation_strings":["Department of Mathematics, Tianjin University, Tianjin 300072, China","Department of mathematics, Tianjin University, Tianjin, 300072 China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Tianjin University, Tianjin 300072, China","institution_ids":["https://openalex.org/I162868743"]},{"raw_affiliation_string":"Department of mathematics, Tianjin University, Tianjin, 300072 China","institution_ids":["https://openalex.org/I162868743"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5029838563","display_name":"Genqi Xu","orcid":"https://orcid.org/0000-0001-8120-0490"},"institutions":[{"id":"https://openalex.org/I162868743","display_name":"Tianjin University","ror":"https://ror.org/012tb2g32","country_code":"CN","type":"education","lineage":["https://openalex.org/I162868743"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Gen Qi Xu","raw_affiliation_strings":["Department of Mathematics, Tianjin University, Tianjin 300072, China","Department of mathematics, Tianjin University, Tianjin, 300072 China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Tianjin University, Tianjin 300072, China","institution_ids":["https://openalex.org/I162868743"]},{"raw_affiliation_string":"Department of mathematics, Tianjin University, Tianjin, 300072 China","institution_ids":["https://openalex.org/I162868743"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100362294","display_name":"Xuan Li","orcid":"https://orcid.org/0000-0002-1138-5335"},"institutions":[{"id":"https://openalex.org/I193524592","display_name":"Tianjin University of Finance and Economics","ror":"https://ror.org/05ev1jb90","country_code":"CN","type":"education","lineage":["https://openalex.org/I193524592"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xuan Li","raw_affiliation_strings":["Department of Mathematics, Pearl River College, Tianjin University of Finance & Economics, Tianjin, 301811, China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Pearl River College, Tianjin University of Finance & Economics, Tianjin, 301811, China","institution_ids":["https://openalex.org/I193524592"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5024753578"],"corresponding_institution_ids":["https://openalex.org/I162868743"],"apc_list":{"value":2582,"currency":"GBP","value_usd":3167},"apc_paid":null,"fwci":0.8115,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.77996481,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"33","issue":"1","first_page":"95","last_page":"119"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.995199978351593,"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.995199978351593,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9693999886512756,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9681000113487244,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/china","display_name":"China","score":0.645497739315033},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.5531757473945618},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.4911760985851288},{"id":"https://openalex.org/keywords/library-science","display_name":"Library science","score":0.4468982517719269},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4013889729976654},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3512282967567444},{"id":"https://openalex.org/keywords/operations-research","display_name":"Operations research","score":0.3258460462093353},{"id":"https://openalex.org/keywords/political-science","display_name":"Political science","score":0.24070122838020325},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.19046086072921753},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.17244946956634521},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.16845914721488953}],"concepts":[{"id":"https://openalex.org/C191935318","wikidata":"https://www.wikidata.org/wiki/Q148","display_name":"China","level":2,"score":0.645497739315033},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5531757473945618},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.4911760985851288},{"id":"https://openalex.org/C161191863","wikidata":"https://www.wikidata.org/wiki/Q199655","display_name":"Library science","level":1,"score":0.4468982517719269},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4013889729976654},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3512282967567444},{"id":"https://openalex.org/C42475967","wikidata":"https://www.wikidata.org/wiki/Q194292","display_name":"Operations research","level":1,"score":0.3258460462093353},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.24070122838020325},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.19046086072921753},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.17244946956634521},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.16845914721488953}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1093/imamci/dnu030","is_oa":false,"landing_page_url":"https://doi.org/10.1093/imamci/dnu030","pdf_url":null,"source":{"id":"https://openalex.org/S162756791","display_name":"IMA Journal of Mathematical Control and Information","issn_l":"0265-0754","issn":["0265-0754","1471-6887"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IMA Journal of Mathematical Control and Information","raw_type":"journal-article"},{"id":"pmh:oai:open-archive.highwire.org:imamci:33/1/95","is_oa":false,"landing_page_url":"http://imamci.oxfordjournals.org/cgi/content/short/33/1/95","pdf_url":null,"source":{"id":"https://openalex.org/S4406923041","display_name":"HighWire Press Open Archive","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"TEXT"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2350270224","https://openalex.org/W2354620178","https://openalex.org/W600967366","https://openalex.org/W2383989146","https://openalex.org/W2351486628","https://openalex.org/W2390481881","https://openalex.org/W2791039681","https://openalex.org/W2329255431","https://openalex.org/W2483714098","https://openalex.org/W2804125163"],"abstract_inverted_index":{"In":[0],"this":[1,94],"paper,":[2],"we":[3,100],"consider":[4],"the":[5,18,21,26,38,49,53,68,71,78,113],"stabilization":[6],"problem":[7],"for":[8],"a":[9,85,102],"wave":[10],"equation":[11],"with":[12,96],"distributed":[13],"controller":[14,23,39],"delay.":[15,91],"Suppose":[16],"that":[17,109],"output":[19],"of":[20,25,48,70,104],"boundary":[22],"is":[24,37,52],"form":[27],"<f>$\\\\alpha":[28],"u(t)+\\\\beta":[29],"u(t-\\\\tau)":[30],"+\\\\int_{-\\\\tau}^{0}":[31],"g(\\\\eta)":[32],"u(t+\\\\eta)\\\\,{\\\\rm":[33],"d}\\\\eta$</f>,":[34],"where":[35],"<it>u</it>(<it>t</it>)":[36],"input,":[40],"<it>\u03b1</it>,":[41],"<it>\u03b2</it>":[42],"\u2208":[43,59],"ℝ":[44],"are":[45],"two":[46],"constants":[47],"controller,":[50],"<it>\u03c4</it>>0":[51],"maximal":[54],"time":[55,90,98],"delay":[56],"and":[57,74],"<it>g</it>(<it>&eegr;</it>)":[58],"<it>L</it>2[\u2212<it>\u03c4</it>,":[60],"0]":[61],"which":[62,87],"does":[63],"not":[64],"equal":[65],"zero.":[66],"Using":[67],"tricks":[69],"Luenberger":[72],"observer":[73],"partial":[75],"state":[76],"predictor,":[77],"delayed":[79,114],"system":[80,86,95],"can":[81,110],"be":[82],"transformed":[83],"to":[84],"has":[88],"no":[89,97],"Based":[92],"on":[93],"delay,":[99],"deduce":[101],"kind":[103],"dynamic":[105],"feedback":[106],"control":[107],"law":[108],"exponentially":[111],"stabilize":[112],"system.":[115]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}