{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,11]],"date-time":"2026-05-11T11:09:30Z","timestamp":1778497770188,"version":"3.51.4"},"reference-count":63,"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"}],"funder":[{"DOI":"10.13039\/501100001659","name":"German Research Foundation","doi-asserted-by":"publisher","award":["HA 10262\/2-1"],"award-info":[{"award-number":["HA 10262\/2-1"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]}],"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>A solution to the suboptimal $H^\\infty $-control problem is given for a class of hyperbolic partial differential equations (PDEs). The first result of this manuscript shows that the considered class of PDEs admits an equivalent representation as an infinite-dimensional discrete-time system. Taking advantage of this, this manuscript shows that it is equivalent to solving the suboptimal $H^\\infty $-control problem for a finite-dimensional discrete-time system whose matrices are derived from the PDEs. After computing the solution to this much simpler problem, the solution to the original problem can be deduced easily. In particular, the optimal compensator solution to the suboptimal $H^\\infty $-control problem is governed by a set of hyperbolic PDEs, actuated and observed at the boundary. We illustrate our results with a boundary-controlled and boundary-observed vibrating string.<\/jats:p>","DOI":"10.1093\/imamci\/dnaf023","type":"journal-article","created":{"date-parts":[[2025,8,23]],"date-time":"2025-08-23T11:38:50Z","timestamp":1755949130000},"source":"Crossref","is-referenced-by-count":1,"title":["<i>H\u221e<\/i>\n                    -control for a class of boundary controlled hyperbolic PDEs"],"prefix":"10.1093","volume":"42","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3776-6339","authenticated-orcid":false,"given":"Anthony","family":"Hastir","sequence":"first","affiliation":[{"name":"School of Mathematics and Natural Sciences, University of Wuppertal , Gau\u00dfstra\u00dfe, 20, 42119 Wuppertal ,","place":["Germany"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8775-4424","authenticated-orcid":false,"given":"Birgit","family":"Jacob","sequence":"additional","affiliation":[{"name":"School of Mathematics and Natural Sciences, University of Wuppertal , Gau\u00dfstra\u00dfe, 20, 42119 Wuppertal ,","place":["Germany"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3451-7967","authenticated-orcid":false,"given":"Hans","family":"Zwart","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, University of Twente , PO Box 217, 7500 AE, Enschede ,","place":["The Netherlands"]},{"name":"Department of Mechanical Engineering, Eindhoven University of Technology , 5600 MB, Eindhoven ,","place":["The Netherlands"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2025,9,10]]},"reference":[{"key":"2026051106114925000_ref1","doi-asserted-by":"publisher","first-page":"1818","DOI":"10.1137\/15M1024901","article-title":"Well-posedness and stability of infinite-dimensional linear port-Hamiltonian systems with nonlinear boundary feedback","volume":"57","author":"Augner","year":"2019","journal-title":"SIAM J. 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