{"id":"https://openalex.org/W1968597120","doi":"https://doi.org/10.1109/acc.2013.6580341","title":"Stabilization of linearized Korteweg-de Vries systems with anti-diffusion","display_name":"Stabilization of linearized Korteweg-de Vries systems with anti-diffusion","publication_year":2013,"publication_date":"2013-06-01","ids":{"openalex":"https://openalex.org/W1968597120","doi":"https://doi.org/10.1109/acc.2013.6580341","mag":"1968597120"},"language":"en","primary_location":{"id":"doi:10.1109/acc.2013.6580341","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2013.6580341","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2013 American Control Conference","raw_type":"proceedings-article"},"type":"conference-paper","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/A5007382527","display_name":"Shu\u2010Xia Tang","orcid":"https://orcid.org/0000-0003-4923-592X"},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Shuxia Tang","raw_affiliation_strings":["Department of Mechanical and Aerospace Engineering, University of California, San Diego, La Jolla, CA, USA","[Dept. of Mech. & Aerosp. Eng., Univ. of California, San Diego, La Jolla, CA, USA]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical and Aerospace Engineering, University of California, San Diego, La Jolla, CA, USA","institution_ids":["https://openalex.org/I36258959"]},{"raw_affiliation_string":"[Dept. of Mech. & Aerosp. Eng., Univ. of California, San Diego, La Jolla, CA, USA]","institution_ids":["https://openalex.org/I36258959"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5018293076","display_name":"Miroslav Krsti\u0107","orcid":"https://orcid.org/0000-0002-5523-941X"},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Miroslav Krstic","raw_affiliation_strings":["Department of Mechanical and Aerospace Engineering, University of California, San Diego, La Jolla, CA, USA","[Dept. of Mech. & Aerosp. Eng., Univ. of California, San Diego, La Jolla, CA, USA]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical and Aerospace Engineering, University of California, San Diego, La Jolla, CA, USA","institution_ids":["https://openalex.org/I36258959"]},{"raw_affiliation_string":"[Dept. of Mech. & Aerosp. Eng., Univ. of California, San Diego, La Jolla, CA, USA]","institution_ids":["https://openalex.org/I36258959"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I36258959"],"apc_list":null,"apc_paid":null,"fwci":1.8703,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.81602286,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"3302","last_page":"3307"},"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/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.9987999796867371,"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"}},{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.996399998664856,"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/backstepping","display_name":"Backstepping","score":0.7972204685211182},{"id":"https://openalex.org/keywords/exponential-stability","display_name":"Exponential stability","score":0.70004802942276},{"id":"https://openalex.org/keywords/semigroup","display_name":"Semigroup","score":0.6273708343505859},{"id":"https://openalex.org/keywords/controller","display_name":"Controller (irrigation)","score":0.5621039867401123},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.560601532459259},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.5581402778625488},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.5559353232383728},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.5103961825370789},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.47138839960098267},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.4624602496623993},{"id":"https://openalex.org/keywords/korteweg\u2013de-vries-equation","display_name":"Korteweg\u2013de Vries equation","score":0.4447157382965088},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.44365575909614563},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4380497932434082},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4058701992034912},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.35828661918640137},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.34794485569000244},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.22243165969848633},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.20440858602523804},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.17958420515060425},{"id":"https://openalex.org/keywords/adaptive-control","display_name":"Adaptive control","score":0.1506185233592987},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.14437219500541687}],"concepts":[{"id":"https://openalex.org/C72218879","wikidata":"https://www.wikidata.org/wiki/Q4839759","display_name":"Backstepping","level":4,"score":0.7972204685211182},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.70004802942276},{"id":"https://openalex.org/C207405024","wikidata":"https://www.wikidata.org/wiki/Q207348","display_name":"Semigroup","level":2,"score":0.6273708343505859},{"id":"https://openalex.org/C203479927","wikidata":"https://www.wikidata.org/wiki/Q5165939","display_name":"Controller (irrigation)","level":2,"score":0.5621039867401123},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.560601532459259},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.5581402778625488},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5559353232383728},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5103961825370789},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.47138839960098267},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.4624602496623993},{"id":"https://openalex.org/C146630112","wikidata":"https://www.wikidata.org/wiki/Q601796","display_name":"Korteweg\u2013de Vries equation","level":3,"score":0.4447157382965088},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.44365575909614563},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4380497932434082},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4058701992034912},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.35828661918640137},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.34794485569000244},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.22243165969848633},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.20440858602523804},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.17958420515060425},{"id":"https://openalex.org/C107464732","wikidata":"https://www.wikidata.org/wiki/Q235781","display_name":"Adaptive control","level":3,"score":0.1506185233592987},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.14437219500541687},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"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/C6557445","wikidata":"https://www.wikidata.org/wiki/Q173113","display_name":"Agronomy","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},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/acc.2013.6580341","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2013.6580341","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2013 American Control Conference","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W564609686","https://openalex.org/W1498121547","https://openalex.org/W1527296550","https://openalex.org/W1980351610","https://openalex.org/W1980366322","https://openalex.org/W2046142489","https://openalex.org/W2098750612","https://openalex.org/W2126464980","https://openalex.org/W2147555499","https://openalex.org/W2178205091","https://openalex.org/W2962709192","https://openalex.org/W3144501209","https://openalex.org/W6630000349"],"related_works":["https://openalex.org/W2771027241","https://openalex.org/W1765905465","https://openalex.org/W2793080664","https://openalex.org/W2186140227","https://openalex.org/W2534185822","https://openalex.org/W2367651125","https://openalex.org/W2387936656","https://openalex.org/W3106150653","https://openalex.org/W2924465594","https://openalex.org/W4386136165"],"abstract_inverted_index":{"In":[0],"this":[1,73],"paper,":[2],"backstepping":[3],"boundary":[4],"controllers":[5],"are":[6],"designed":[7],"for":[8],"a":[9],"class":[10],"of":[11,31,41,53,64],"linearized":[12],"Korteweg-de":[13],"Vries":[14],"systems":[15,23],"with":[16],"possible":[17],"anti-diffusion,":[18],"and":[19,39,45],"the":[20,42,65,87],"resulting":[21],"closed-loop":[22],"can":[24,83],"achieve":[25],"arbitrary":[26],"exponential":[27],"decay":[28,68,80],"rate.":[29],"Semigroup":[30],"linear":[32],"operators":[33],"is":[34,48,58,75],"constructed":[35],"in":[36,50,72],"analyzing":[37],"well-posedness":[38],"stability":[40],"target":[43],"systems,":[44],"mathematical":[46],"induction":[47],"used":[49],"proving":[51],"existence":[52],"kernel":[54],"functions.":[55],"An":[56],"example":[57],"also":[59],"presented,":[60],"which":[61,82],"illustrates":[62],"performance":[63],"controller.":[66],"The":[67],"rate":[69],"estimate":[70],"derived":[71],"paper":[74],"not":[76],"necessarily":[77],"equal":[78],"to":[79],"rate,":[81],"be":[84],"seen":[85],"from":[86],"appendix.":[88]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2}],"updated_date":"2026-08-11T07:18:39.950985","created_date":"2025-10-10T00:00:00"}