{"id":"https://openalex.org/W2027500128","doi":"https://doi.org/10.1109/tac.2012.2204837","title":"Strong Stability of an Unstable Wave Equation by Boundary Feedback With Only Displacement Observation","display_name":"Strong Stability of an Unstable Wave Equation by Boundary Feedback With Only Displacement Observation","publication_year":2012,"publication_date":"2012-06-14","ids":{"openalex":"https://openalex.org/W2027500128","doi":"https://doi.org/10.1109/tac.2012.2204837","mag":"2027500128"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2012.2204837","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2012.2204837","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","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/A5063671825","display_name":"Wei Guo","orcid":"https://orcid.org/0000-0002-4917-8737"},"institutions":[{"id":"https://openalex.org/I146563203","display_name":"University of International Business and Economics","ror":"https://ror.org/05khqpb71","country_code":"CN","type":"education","lineage":["https://openalex.org/I146563203"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Wei Guo","raw_affiliation_strings":["School of Information Technology and Management and China Service Industry Research Center, University of International Business and Economics, Beijing, China","Sch. of Inf. Technol. & Manage., Univ. of Int. Bus. & Econ., Beijing, China"],"affiliations":[{"raw_affiliation_string":"School of Information Technology and Management and China Service Industry Research Center, University of International Business and Economics, Beijing, China","institution_ids":["https://openalex.org/I146563203"]},{"raw_affiliation_string":"Sch. of Inf. Technol. & Manage., Univ. of Int. Bus. & Econ., Beijing, China","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5053284380","display_name":"Zhi\u2010Chao Shao","orcid":null},"institutions":[{"id":"https://openalex.org/I146563203","display_name":"University of International Business and Economics","ror":"https://ror.org/05khqpb71","country_code":"CN","type":"education","lineage":["https://openalex.org/I146563203"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhi-Chao Shao","raw_affiliation_strings":["School of Information Technology and Management and China Service Industry Research Center, University of International Business and Economics, Beijing, China","Sch. of Inf. Technol. & Manage., Univ. of Int. Bus. & Econ., Beijing, China"],"affiliations":[{"raw_affiliation_string":"School of Information Technology and Management and China Service Industry Research Center, University of International Business and Economics, Beijing, China","institution_ids":["https://openalex.org/I146563203"]},{"raw_affiliation_string":"Sch. of Inf. Technol. & Manage., Univ. of Int. Bus. & Econ., Beijing, China","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5063671825"],"corresponding_institution_ids":["https://openalex.org/I146563203"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.10387974,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"57","issue":"9","first_page":"2367","last_page":"2372"},"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":1.0,"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":1.0,"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.991599977016449,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.9847999811172485,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/backstepping","display_name":"Backstepping","score":0.7132839560508728},{"id":"https://openalex.org/keywords/controller","display_name":"Controller (irrigation)","score":0.5988886952400208},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.5889572501182556},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.5775993466377258},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.5298761129379272},{"id":"https://openalex.org/keywords/displacement","display_name":"Displacement (psychology)","score":0.5284756422042847},{"id":"https://openalex.org/keywords/exponential-stability","display_name":"Exponential stability","score":0.512904167175293},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4919869601726532},{"id":"https://openalex.org/keywords/semigroup","display_name":"Semigroup","score":0.47582772374153137},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4146018624305725},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.40293988585472107},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.27856677770614624},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2315560281276703},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.2163405418395996},{"id":"https://openalex.org/keywords/adaptive-control","display_name":"Adaptive control","score":0.11553317308425903},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.07774996757507324}],"concepts":[{"id":"https://openalex.org/C72218879","wikidata":"https://www.wikidata.org/wiki/Q4839759","display_name":"Backstepping","level":4,"score":0.7132839560508728},{"id":"https://openalex.org/C203479927","wikidata":"https://www.wikidata.org/wiki/Q5165939","display_name":"Controller (irrigation)","level":2,"score":0.5988886952400208},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5889572501182556},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5775993466377258},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.5298761129379272},{"id":"https://openalex.org/C107551265","wikidata":"https://www.wikidata.org/wiki/Q1458245","display_name":"Displacement (psychology)","level":2,"score":0.5284756422042847},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.512904167175293},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4919869601726532},{"id":"https://openalex.org/C207405024","wikidata":"https://www.wikidata.org/wiki/Q207348","display_name":"Semigroup","level":2,"score":0.47582772374153137},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4146018624305725},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.40293988585472107},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.27856677770614624},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2315560281276703},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.2163405418395996},{"id":"https://openalex.org/C107464732","wikidata":"https://www.wikidata.org/wiki/Q235781","display_name":"Adaptive control","level":3,"score":0.11553317308425903},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.07774996757507324},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.0},{"id":"https://openalex.org/C6557445","wikidata":"https://www.wikidata.org/wiki/Q173113","display_name":"Agronomy","level":1,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C542102704","wikidata":"https://www.wikidata.org/wiki/Q183257","display_name":"Psychotherapist","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tac.2012.2204837","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2012.2204837","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","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":12,"referenced_works":["https://openalex.org/W1995358042","https://openalex.org/W2000679573","https://openalex.org/W2004690759","https://openalex.org/W2030958501","https://openalex.org/W2050873846","https://openalex.org/W2091562669","https://openalex.org/W2097618054","https://openalex.org/W2104655522","https://openalex.org/W2110837625","https://openalex.org/W2137817450","https://openalex.org/W2168279726","https://openalex.org/W3144501209"],"related_works":["https://openalex.org/W1765905465","https://openalex.org/W2924465594","https://openalex.org/W3106150653","https://openalex.org/W4386136165","https://openalex.org/W2164703465","https://openalex.org/W2168383058","https://openalex.org/W2143247663","https://openalex.org/W1864017312","https://openalex.org/W2050693590","https://openalex.org/W4313442219"],"abstract_inverted_index":{"The":[0,22,41,49],"stabilization":[1],"of":[2,43],"a":[3],"1-D":[4],"wave":[5],"equation":[6],"that":[7,30,36,65],"contains":[8],"instability":[9],"at":[10,16],"its":[11],"free":[12],"end":[13,19],"and":[14,58],"control":[15],"the":[17,27,34,66],"other":[18],"is":[20,24,31,39,45,69],"considered.":[21],"controller":[23],"designed":[25,32],"through":[26],"estimated":[28],"state":[29],"in":[33,47],"case":[35],"only":[37],"displacement":[38],"available.":[40],"method":[42,60],"\u201cbackstepping\u201d":[44],"adopted":[46],"investigation.":[48],"<i":[50],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[51,54],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">C</i>":[52],"<sub":[53],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">0</sub>":[55],"-semigroup":[56],"theory":[57],"Lyapunov":[59],"are":[61],"used":[62],"to":[63],"show":[64],"closed-loop":[67],"system":[68],"asymptotically":[70],"stable.":[71]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}