{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,3]],"date-time":"2026-01-03T06:46:24Z","timestamp":1767422784770,"version":"3.37.3"},"reference-count":19,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2019,9,5]],"date-time":"2019-09-05T00:00:00Z","timestamp":1567641600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61603226"],"award-info":[{"award-number":["61603226"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2020,9,16]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>In this paper, we are concerned with boundary output feedback stabilization of a transport equation with non-local term. First, a boundary state feedback controller is designed by a backstepping approach. The closed-loop system is proved to be exponentially stable by the equivalence between original and target system. Then, we design an output feedback controller based on an infinite-dimensional observer. It is shown that the result closed-loop system is also exponentially stable. Finally, some numerical examples are presented to illustrate the effectiveness of the proposed feedback controller.<\/jats:p>","DOI":"10.1093\/imamci\/dnz022","type":"journal-article","created":{"date-parts":[[2019,6,27]],"date-time":"2019-06-27T11:09:28Z","timestamp":1561633768000},"page":"752-764","source":"Crossref","is-referenced-by-count":3,"title":["Boundary output feedback stabilization of transport equation with non-local term"],"prefix":"10.1093","volume":"37","author":[{"given":"Liping","family":"Wang","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, China"}]},{"given":"Feng-Fei","family":"Jin","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, China"}]}],"member":"286","published-online":{"date-parts":[[2019,9,5]]},"reference":[{"key":"2021060109593146300_ref1","doi-asserted-by":"crossref","first-page":"2145","DOI":"10.1109\/TAC.2015.2398882","article-title":"Backstepping-forwarding control and observation for hyperbolic PDEs with fredholm integrals","volume":"60","author":"Argomedo","year":"2015","journal-title":"IEEE Trans. Automat. Control"},{"key":"2021060109593146300_ref2","doi-asserted-by":"crossref","first-page":"2692","DOI":"10.1016\/j.automatica.2014.09.001","article-title":"Adaptive output-feedback stabilization of non-local hyperbolic PDEs","volume":"50","author":"Bernard","year":"2014","journal-title":"Automatica J. IFAC"},{"volume-title":"Control and Nonlinearity","year":"2007","author":"Coron","key":"2021060109593146300_ref3"},{"key":"2021060109593146300_ref4","first-page":"2005","article-title":"Local exponential ${H}^2$ stabilization of a $2\\times 2$ quasilinear hyperbolic system using backstepping","volume-title":"SIAM J. Control Optim.","author":"Coron","year":"2013"},{"key":"2021060109593146300_ref5","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1007\/BF02065450","article-title":"Physical interpretation of the boundary conditions for isothermal hyperbolic reactors","volume":"16","author":"Holderith","year":"1981","journal-title":"React. Kinet. Catalysis Lett."},{"key":"2021060109593146300_ref6","doi-asserted-by":"crossref","DOI":"10.1137\/1.9780898718607","volume-title":"Boundary Control of PDEs: A Course on Backstepping Designs","author":"Krstic","year":"2008"},{"key":"2021060109593146300_ref7","doi-asserted-by":"crossref","DOI":"10.1007\/978-0-8176-4877-0","volume-title":"Delay Compensation for Nonlinear, Adaptive, and PDE Systems","author":"Krstic","year":"2009"},{"key":"2021060109593146300_ref8","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1016\/j.automatica.2007.05.012","article-title":"Output-feedback stabilization of an unstable wave equation","volume":"44","author":"Krstic","year":"2008","journal-title":"Automatica J. IFAC"},{"key":"2021060109593146300_ref9","doi-asserted-by":"crossref","first-page":"553","DOI":"10.1137\/060676969","article-title":"Control of a tip-force destabilized shear beam by non-collocated observer-based boundary feedback","volume":"47","author":"Krstic","year":"2008","journal-title":"SIAM J. Control Optim."},{"key":"2021060109593146300_ref10","doi-asserted-by":"crossref","first-page":"750","DOI":"10.1016\/j.sysconle.2008.02.005","article-title":"Backstepping boundary control for first order hyperbolic PDEs and application to systems with actuator and sensor delays","volume":"57","author":"Krstic","year":"2008","journal-title":"Systems Control Lett."},{"key":"2021060109593146300_ref11","doi-asserted-by":"crossref","first-page":"3097","DOI":"10.1109\/TAC.2013.2274723","volume":"58","author":"Meglio","year":"2013","journal-title":"IEEE Trans. Automat. Control"},{"key":"2021060109593146300_ref12","doi-asserted-by":"crossref","first-page":"4760","DOI":"10.1109\/TAC.2017.2688128","article-title":"Boundary stabilization of wave equation with velocity recirculation","volume":"62","author":"Su","year":"2017","journal-title":"IEEE Trans. Automat. Control"},{"key":"2021060109593146300_ref13","doi-asserted-by":"crossref","first-page":"2185","DOI":"10.1109\/TAC.2004.838495","article-title":"Closed form boundary state feedbacks for a class of 1-D partial integro-differential equations","volume":"49","author":"Smyshlyaev","year":"2004","journal-title":"IEEE Trans. Automat. Control"},{"key":"2021060109593146300_ref14","doi-asserted-by":"crossref","first-page":"2202","DOI":"10.1109\/ACC.2012.6314688","article-title":"Collocated output\u2013feedback stabilization of a $2\\times 2$ quasilinear hyperbolic system using backstepping","author":"Vazquez","year":"2012","journal-title":"2012 American Control Conference"},{"key":"2021060109593146300_ref15","doi-asserted-by":"crossref","first-page":"2298","DOI":"10.1109\/TAC.2007.910686","article-title":"A closed-form feedback controller for stabilization of the linearized 2-D Navier-stokes Poiseuille flow","volume":"52","author":"Vazquez","year":"2007","journal-title":"IEEE Trans. Automat. Control"},{"key":"2021060109593146300_ref16","first-page":"421","article-title":"Exponential stability and transfer functions of processes governed by symmetric hyperbolic systems","volume":"7","author":"Xu","year":"2002","journal-title":"ESAIM: Control Optim. Calc. Var."},{"key":"2021060109593146300_ref17","doi-asserted-by":"crossref","first-page":"448","DOI":"10.1016\/j.automatica.2012.11.005","article-title":"Stabilization of linear heat equation with a heat source at intermediate point by boundary control","volume":"49","author":"Zhou","year":"2013","journal-title":"Automatica J. IFAC"},{"key":"2021060109593146300_ref18","first-page":"1377","article-title":"Stabilization of a coupled second order ODE-wave system. 35th Chinese Control Conference, 2016","author":"Zhen","year":"2016"},{"key":"2021060109593146300_ref19","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1016\/j.automatica.2015.06.039","article-title":"Stabilization of a second order ODE-heat system coupling at intermediate point","volume":"60","author":"Zhou","year":"2015","journal-title":"Automatica J. IFAC"}],"container-title":["IMA Journal of Mathematical Control and Information"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/academic.oup.com\/imamci\/article-pdf\/37\/3\/752\/38390522\/imamci_37_3_752.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"http:\/\/academic.oup.com\/imamci\/article-pdf\/37\/3\/752\/38390522\/imamci_37_3_752.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,6,1]],"date-time":"2021-06-01T10:22:44Z","timestamp":1622542964000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/imamci\/article\/37\/3\/752\/5560307"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,9,5]]},"references-count":19,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2019,9,5]]},"published-print":{"date-parts":[[2020,9,16]]}},"URL":"https:\/\/doi.org\/10.1093\/imamci\/dnz022","relation":{},"ISSN":["0265-0754","1471-6887"],"issn-type":[{"type":"print","value":"0265-0754"},{"type":"electronic","value":"1471-6887"}],"subject":[],"published-other":{"date-parts":[[2020,9]]},"published":{"date-parts":[[2019,9,5]]}}}