{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,11,19]],"date-time":"2024-11-19T18:06:34Z","timestamp":1732039594757},"reference-count":38,"publisher":"Oxford University Press (OUP)","issue":"4","license":[{"start":{"date-parts":[[2020,9,23]],"date-time":"2020-09-23T00:00:00Z","timestamp":1600819200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2020,12,16]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>This paper considers the well posedness and the exponential stabilization problems of a cascaded ordinary differential equation (ODE)\u2013partial differential equation (PDE) system. The considered system is governed by a linear ODE and the one-dimensional linear Korteweg\u2013de Vries (KdV) equation posed on a bounded interval. For the whole system, a control input delay acts on the left boundary of the KdV domain by Dirichlet condition. Whereas, the KdV acts back on the ODE by Dirichlet interconnection on the right boundary. Firstly, we reformulate the system in question as an undelayed ODE-coupled KdV-transport system. Secondly, we use the so-called infinite dimensional backstepping method to derive an explicit feedback control law that transforms system under consideration to a well-posed and exponentially stable target system. Finally, by invertibility of such design, we use semigroup theory and Lyapunov analysis to prove the well posedness and the exponential stabilization in a suitable functional space of the original plant, respectively.<\/jats:p>","DOI":"10.1093\/imamci\/dnaa022","type":"journal-article","created":{"date-parts":[[2020,9,3]],"date-time":"2020-09-03T11:11:52Z","timestamp":1599131512000},"page":"1506-1523","source":"Crossref","is-referenced-by-count":3,"title":["Exponential stabilization of an ODE\u2013linear KdV cascaded system with boundary input delay"],"prefix":"10.1093","volume":"37","author":[{"given":"Habib","family":"Ayadi","sequence":"first","affiliation":[{"name":"Higher Institute of Applied Mathematics and Computer Science, University of Kairouan, Assad Iben Fourat Avenue, 3100 Kairouan, Tunisia"}]}],"member":"286","published-online":{"date-parts":[[2020,9,23]]},"reference":[{"key":"2020121600534915800_ref1","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1007\/s00028-009-0004-z","article-title":"Feedback stabilization of a class of evolution equations with delay","volume":"9","author":"Ait Benhassi","year":"2009","journal-title":"J. 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