{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,20]],"date-time":"2025-09-20T21:57:18Z","timestamp":1758405438884,"version":"3.41.2"},"reference-count":70,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2021,4,12]],"date-time":"2021-04-12T00:00:00Z","timestamp":1618185600000},"content-version":"vor","delay-in-days":101,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62003275","U1911401","62073088","U1701261"],"award-info":[{"award-number":["62003275","U1911401","62073088","U1701261"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["31020190QD039"],"award-info":[{"award-number":["31020190QD039"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2021,1]]},"abstract":"<jats:p>In this paper, a robust <jats:italic>H<\/jats:italic><jats:sub><jats:italic>\u221e<\/jats:italic><\/jats:sub> control problem of a class of linear parabolic distributed parameter systems (DPSs) with pointwise\/piecewise control and pointwise\/piecewise measurement has been investigated via the robust <jats:italic>H<\/jats:italic><jats:sub><jats:italic>\u221e<\/jats:italic><\/jats:sub> feedback compensator design approach. A unified Lyapunov direct approach is proposed in consideration of the pointwise\/piecewise control and point\/piecewise measurement based on the distributions of the actuators and sensors. A new type of Luenberger observer is developed on the continuous interval of space domain to track the state of the system, and an <jats:italic>H<\/jats:italic><jats:sub><jats:italic>\u221e<\/jats:italic><\/jats:sub> performance constraint with prescribed <jats:italic>H<\/jats:italic><jats:sub><jats:italic>\u221e<\/jats:italic><\/jats:sub> attenuation levels is proposed in this paper. By utilizing Lyapunov technique, mathematical inequalities, and integration theory, a sufficient condition based on LMI for the exponential stability of the corresponding closed\u2010loop coupled system under an <jats:italic>H<\/jats:italic><jats:sub><jats:italic>\u221e<\/jats:italic><\/jats:sub> performance constraint is presented. Finally, the effectiveness of the proposed design method is verified by numerical simulation results.<\/jats:p>","DOI":"10.1155\/2021\/6660857","type":"journal-article","created":{"date-parts":[[2021,4,12]],"date-time":"2021-04-12T20:21:30Z","timestamp":1618258890000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Robust <i>H<\/i><sub><i>\u221e<\/i><\/sub> Feedback Compensator Design for Linear Parabolic DPSs with Pointwise\/Piecewise Control and Pointwise\/Piecewise Measurement"],"prefix":"10.1155","volume":"2021","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1409-7352","authenticated-orcid":false,"given":"Liu","family":"Yaqiang","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0913-0130","authenticated-orcid":false,"given":"Ren","family":"Zhigang","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7491-9103","authenticated-orcid":false,"given":"Jin","family":"Zengwang","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2021,4,12]]},"reference":[{"key":"e_1_2_9_1_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0185-4"},{"key":"e_1_2_9_2_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-007-0741-2"},{"key":"e_1_2_9_3_2","doi-asserted-by":"publisher","DOI":"10.1109\/tie.2018.2818645"},{"key":"e_1_2_9_4_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-18258-7"},{"key":"e_1_2_9_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.arcontrol.2009.01.003"},{"key":"e_1_2_9_6_2","doi-asserted-by":"crossref","first-page":"684","DOI":"10.1109\/TNNLS.2014.2320744","article-title":"Adaptive 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