{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,4]],"date-time":"2026-05-04T16:00:12Z","timestamp":1777910412865,"version":"3.51.4"},"reference-count":28,"publisher":"SAGE Publications","issue":"1","license":[{"start":{"date-parts":[[2018,4,18]],"date-time":"2018-04-18T00:00:00Z","timestamp":1524009600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61673061"],"award-info":[{"award-number":["61673061"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Transactions of the Institute of Measurement and Control"],"published-print":{"date-parts":[[2019,1]]},"abstract":"<jats:p>Output regulation is considered in this paper for ordinary differential equations cascaded by a wave equation, in which both the body equations and the uncontrolled end are subject to disturbances. The disturbances are generated by an exosystem. A backstepping state-feedback regulator is first designed to force the output to track the reference signal. The design is based on solving cascaded regulator equations, and the solvability condition of the equations is characterized in terms of a transfer function and the eigenvalues of the exosystem. An observer-based output-feedback regulator is then designed to solve the output regulation problem. Finally, the regulator tracking performance is illustrated through numerical simulations.<\/jats:p>","DOI":"10.1177\/0142331217752040","type":"journal-article","created":{"date-parts":[[2018,4,18]],"date-time":"2018-04-18T17:55:38Z","timestamp":1524074138000},"page":"246-262","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":11,"title":["Backstepping-based output regulation of ordinary differential equations cascaded by wave equation with in-domain anti-damping"],"prefix":"10.1177","volume":"41","author":[{"given":"Jianjun","family":"Gu","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, China"},{"name":"School of Mathematics and Statistics, Changshu Institute of Technology, Jiangsu, China"}]},{"given":"Chunqiu","family":"Wei","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, China"}]},{"given":"Junmin","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, China"}]}],"member":"179","published-online":{"date-parts":[[2018,4,18]]},"reference":[{"key":"bibr1-0142331217752040","doi-asserted-by":"publisher","DOI":"10.1177\/0142331216661621"},{"key":"bibr2-0142331217752040","volume-title":"Sobolev Spaces","author":"Adams RA","year":"2003"},{"key":"bibr3-0142331217752040","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2014.2322435"},{"key":"bibr4-0142331217752040","volume-title":"A Practical Guide to Geometric Regulation for Distributed Parameter Systems","author":"Aulisa E","year":"2016"},{"key":"bibr5-0142331217752040","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-84800-344-6"},{"key":"bibr6-0142331217752040","doi-asserted-by":"publisher","DOI":"10.1007\/s10957-007-9223-z"},{"key":"bibr7-0142331217752040","doi-asserted-by":"publisher","DOI":"10.1137\/060671188"},{"key":"bibr8-0142331217752040","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2015.2491718"},{"key":"bibr9-0142331217752040","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2016.09.020"},{"key":"bibr10-0142331217752040","doi-asserted-by":"publisher","DOI":"10.1109\/CDC.2014.7039701"},{"key":"bibr11-0142331217752040","doi-asserted-by":"publisher","DOI":"10.1177\/0142331216637117"},{"key":"bibr12-0142331217752040","doi-asserted-by":"publisher","DOI":"10.1002\/pamm.201610012"},{"key":"bibr13-0142331217752040","doi-asserted-by":"publisher","DOI":"10.1007\/b139040"},{"key":"bibr14-0142331217752040","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898718607"},{"key":"bibr15-0142331217752040","doi-asserted-by":"publisher","DOI":"10.1137\/070704290"},{"key":"bibr16-0142331217752040","volume-title":"Control Theory for Partial Differential Equations: Continuous and Approximation Theories. 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