{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:59:16Z","timestamp":1787324356814,"version":"build-2736575974"},"reference-count":29,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","funder":[{"name":"ANID-Basal","award":["FB0008 AC3E"],"award-info":[{"award-number":["FB0008 AC3E"]}]},{"DOI":"10.13039\/501100002850","name":"Fondo Nacional de Desarrollo Cient\u00edfico y Tecnol\u00f3gico","doi-asserted-by":"publisher","award":["1180528"],"award-info":[{"award-number":["1180528"]}],"id":[{"id":"10.13039\/501100002850","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002848","name":"Comisi\u00f3n Nacional de Investigaci\u00f3n Cient\u00edfica y Tecnol\u00f3gica","doi-asserted-by":"publisher","award":["C16E06"],"award-info":[{"award-number":["C16E06"]}],"id":[{"id":"10.13039\/501100002848","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Control Optim."],"published-print":{"date-parts":[[2021,1]]},"abstract":"<jats:p>This paper is about the stabilization of a cascade system of $n$ linear Korteweg--de Vries equations in a bounded interval. It considers an output feedback control placed at the left endpoint of the last equation, while the output involves only the solution to the first equation. The boundary control problems investigated include two cases: a classical control on the Dirichlet boundary condition and a less standard one on its second-order derivative. The feedback control law utilizes the estimated solutions of a high-gain observer system, and the output feedback control leads to stabilization for any $n$ for the first boundary conditions case and for $n=2$ for the second one.<\/jats:p>","DOI":"10.1137\/20m1350066","type":"journal-article","created":{"date-parts":[[2021,8,19]],"date-time":"2021-08-19T12:17:42Z","timestamp":1629375462000},"page":"2955-2976","source":"Crossref","is-referenced-by-count":0,"title":["Output Feedback Control of a Cascade System of Linear Korteweg--de Vries Equations"],"prefix":"10.1137","volume":"59","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5108-090X","authenticated-orcid":true,"given":"Constantinos","family":"Kitsos","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Eduardo","family":"Cerpa","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Gildas","family":"Besan\u00e7on","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4456-2019","authenticated-orcid":true,"given":"Christophe","family":"Prieur","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2021,8,19]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1137\/15M1015765"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2019.108531"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.3934\/mcrf.2014.4.45"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2013.2241479"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1142\/S021919971100418X"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1137\/120891721"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1016\/j.matpur.2014.03.004"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1137\/120875739"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1051\/cocv\/2014063"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1016\/S0898-1221(03)00018-X"},{"key":"atypb11","first-page":"871","author":"Hasan A.","year":"2016","journal-title":"Greece"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1016\/0375-9601(81)90423-0"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2016.06.063"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1051\/cocv\/2018057"},{"key":"atypb15","doi-asserted-by":"crossref","unstructured":"H. K. Khalil,\n                      High-Gain Observers in Nonlinear Feedback Control\n                      , Adv. Des. Control, SIAM, Philadelphia, PA, 2017.","DOI":"10.1137\/1.9781611974867"},{"key":"atypb16","unstructured":"C. Kitsos,\n                      High-Gain Observer Design for System of PDEs\n                      , PhD thesis, Automatic Control Engineering, University Grenoble-Alpes, 2020."},{"key":"atypb17","author":"Kitsos C.","journal-title":"IEEE Trans. Automat. Control, in press."},{"key":"atypb18","doi-asserted-by":"crossref","unstructured":"C. Kitsos, G. Besan\u00e7on, and C. Prieur,\n                      Contributions to the problem of high-gain observer design for hyperbolic systems\n                      , in Trends in Nonlinear and Adaptive Control: A Tribute to Laurent Praly for His 65th Birthday, Lect. Notes Control Inf. Sci., Springer, Cham, 2021.","DOI":"10.1007\/978-3-030-74628-5_5"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1137\/17M1119160"},{"key":"atypb20","first-page":"513","volume":"39","author":"Lou S. Y.","year":"2006","journal-title":"Gen."},{"key":"atypb21","doi-asserted-by":"crossref","unstructured":"S. Marx and E. Cerpa,\n                      Output feedback control of the linear Korteweg-de Vries equation\n                      , in Proceedings of the 53rd IEEE Conference on Decision and Control, Los Angeles, CA, 2014, pp. 2083-2087.","DOI":"10.1109\/CDC.2014.7039705"},{"key":"atypb22","doi-asserted-by":"publisher","DOI":"10.1137\/16M1061837"},{"key":"atypb23","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2017.07.057"},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1090\/qam\/1878262"},{"key":"atypb25","doi-asserted-by":"publisher","DOI":"10.1051\/cocv:2004012"},{"key":"atypb26","doi-asserted-by":"publisher","DOI":"10.1007\/s11424-009-9194-2"},{"key":"atypb27","first-page":"3302","author":"Tang S.","year":"2013","journal-title":"Washington, DC"},{"key":"atypb28","first-page":"1959","author":"Tang S.","year":"2015","journal-title":"Chicago"},{"key":"atypb29","first-page":"371","volume":"118","author":"Zhang B.-Y.","year":"1994","journal-title":"Internat. Series Numer. Math."}],"container-title":["SIAM Journal on Control and Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/20M1350066","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:22:27Z","timestamp":1787322147000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/20M1350066"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,1]]},"references-count":29,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2021,1]]}},"alternative-id":["10.1137\/20M1350066"],"URL":"https:\/\/doi.org\/10.1137\/20m1350066","relation":{},"ISSN":["0363-0129","1095-7138"],"issn-type":[{"value":"0363-0129","type":"print"},{"value":"1095-7138","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,1]]}}}