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First, we choose a well\u2010known exponentially stable system as its target system and find a backstepping transformation to design a state feedback controller for the original system. Second, we attempt to give an output feedback controller for the original system by introducing the observer. The resulting closed\u2010loop system admits a unique solution which is proved to be exponentially stable. Finally, we give some numerical examples to prove the validity for the theoretical results.<\/jats:p>","DOI":"10.1155\/2021\/9977714","type":"journal-article","created":{"date-parts":[[2021,6,4]],"date-time":"2021-06-04T18:41:28Z","timestamp":1622832088000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Boundary Output Feedback Stabilization for a Cascaded\u2010Wave PDE\u2010ODE System with Velocity Recirculation"],"prefix":"10.1155","volume":"2021","author":[{"given":"Ruicheng","family":"Li","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9448-8630","authenticated-orcid":false,"given":"Feng-Fei","family":"Jin","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6601-6433","authenticated-orcid":false,"given":"Baoqiang","family":"Yan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2021,6,4]]},"reference":[{"key":"e_1_2_9_1_2","doi-asserted-by":"publisher","DOI":"10.1109\/tac.2019.2937727"},{"key":"e_1_2_9_2_2","doi-asserted-by":"publisher","DOI":"10.1109\/tac.2014.2335374"},{"key":"e_1_2_9_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ifacsc.2020.100100"},{"key":"e_1_2_9_4_2","doi-asserted-by":"publisher","DOI":"10.1109\/tac.2019.2941431"},{"key":"e_1_2_9_5_2","doi-asserted-by":"publisher","DOI":"10.1002\/zamm.201900013"},{"key":"e_1_2_9_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejcon.2017.10.006"},{"key":"e_1_2_9_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2017.03.043"},{"key":"e_1_2_9_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.sysconle.2020.104780"},{"key":"e_1_2_9_9_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11424-013-2070-0"},{"key":"e_1_2_9_10_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfranklin.2011.06.008"},{"key":"e_1_2_9_11_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.sysconle.2011.04.011"},{"key":"e_1_2_9_12_2","doi-asserted-by":"crossref","unstructured":"TangS. 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