{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,11]],"date-time":"2026-05-11T11:09:35Z","timestamp":1778497775773,"version":"3.51.4"},"reference-count":28,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2025,7,23]],"date-time":"2025-07-23T00:00:00Z","timestamp":1753228800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025,7,23]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>This work considers the output regulation problem for an infinite-dimensional system. Specifically, a regulator for boundary-controlled time-varying $2\\times 2$ hyperbolic systems is designed. The output regulation is solved in finite time. Moreover, the disturbances can act within the space domain, and affect both boundaries and the to-be-controlled output. The to-be-controlled output is pointwise and may be located either at the boundary or at any point inside of the space domain. The feedback gain is a time-dependent function rather than a constant vector. Time-varying setting also brings an advantage to the problem, since the solvability of the regulator equations does not depend on the eigenmodes of the signal model. In this work, the regulator equations have a solution for any signal model. The finite-time reference signal and disturbance observer are also designed. The output feedback regulator consists of the state feedback regulator and the finite-time observer. A numerical example illustrates the regulator design and the finite-time regulation.<\/jats:p>","DOI":"10.1093\/imamci\/dnaf024","type":"journal-article","created":{"date-parts":[[2025,8,21]],"date-time":"2025-08-21T11:54:14Z","timestamp":1755777254000},"source":"Crossref","is-referenced-by-count":0,"title":["Finite-time output regulation for time-varying\n                    <i>2 \u00d7 2<\/i>\n                    hyperbolic systems"],"prefix":"10.1093","volume":"42","author":[{"given":"Yubo","family":"Bai","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, Fudan University , Shanghai 200433 ,","place":["China"]},{"name":"Univversity Grenoble Alpes, CNRS , Grenoble-INP, GIPSA-Lab, F-38000 Grenoble ,","place":["France"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Christophe","family":"Prieur","sequence":"additional","affiliation":[{"name":"Univversity Grenoble Alpes, CNRS , Grenoble-INP, GIPSA-Lab, F-38000 Grenoble ,","place":["France"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhiqiang","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Shanghai Key Laboratory for Contemporary Applied Mathematics, Fudan University , Shanghai 200433 ,","place":["China"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2025,9,10]]},"reference":[{"key":"2026051106115544500_ref1","volume-title":"Analyse num\u00e9rique et Optimisation","author":"Allaire","year":"2005"},{"key":"2026051106115544500_ref2","doi-asserted-by":"publisher","first-page":"186","DOI":"10.1109\/TAC.2014.2322435","article-title":"Disturbance rejection in the interior domain of linear 2 $\\times $ 2 hyperbolic systems","volume":"60","author":"Anfinsen","year":"2015","journal-title":"IEEE Trans. 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