{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,4]],"date-time":"2026-05-04T20:41:17Z","timestamp":1777927277372,"version":"3.51.4"},"reference-count":31,"publisher":"SAGE Publications","issue":"4","license":[{"start":{"date-parts":[[2020,8,11]],"date-time":"2020-08-11T00:00:00Z","timestamp":1597104000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"funder":[{"DOI":"10.13039\/100007224","name":"national foundation for science and technology development","doi-asserted-by":"publisher","award":["101.02-2020.08"],"award-info":[{"award-number":["101.02-2020.08"]}],"id":[{"id":"10.13039\/100007224","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering"],"published-print":{"date-parts":[[2021,4]]},"abstract":"<jats:p>This article considers the estimation problem for a class of uncertain fractional-order systems with time-varying delays and disturbances, in which the time-varying delays are present in the state, while the disturbances are present in the output. A new design method of functional interval observers is proposed. In contrast to interval observers currently available in the literature, which dealt with integer-order systems or fractional-order systems without time delays, the functional interval observers with fractional-order [Formula: see text] in this article can deal with fractional-order time-delay systems and integer-order time-delay systems (when [Formula: see text]). Existence conditions of functional interval observers for non-linear fractional-order systems with time-varying delays are established and they are formulated in terms of linear programmings. Two algorithms are provided for determining the functional interval observers. Illustrative examples of the functional interval observer application are presented.<\/jats:p>","DOI":"10.1177\/0959651820945828","type":"journal-article","created":{"date-parts":[[2020,8,11]],"date-time":"2020-08-11T03:14:41Z","timestamp":1597115681000},"page":"550-562","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":7,"title":["Functional interval observers for nonlinear fractional-order systems with time-varying delays and disturbances"],"prefix":"10.1177","volume":"235","author":[{"given":"Dao Thi Hai","family":"Yen","sequence":"first","affiliation":[{"name":"Department of Sciences, Phu Yen University, Tuy Hoa, Vietnam"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2028-3784","authenticated-orcid":false,"given":"Dinh Cong","family":"Huong","sequence":"additional","affiliation":[{"name":"Department for Management of Science and Technology Development, Ton Duc Thang University, Ho Chi Minh City, Vietnam"},{"name":"Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2020,8,11]]},"reference":[{"key":"bibr1-0959651820945828","doi-asserted-by":"publisher","DOI":"10.1109\/TCSI.2010.2096111"},{"key":"bibr2-0959651820945828","doi-asserted-by":"publisher","DOI":"10.1016\/j.physleta.2006.01.068"},{"key":"bibr3-0959651820945828","volume-title":"Fractional differential equations","author":"Podlubny I.","year":"1999"},{"key":"bibr4-0959651820945828","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.62.3135"},{"key":"bibr5-0959651820945828","doi-asserted-by":"publisher","DOI":"10.1063\/1.1535007"},{"key":"bibr6-0959651820945828","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2011.02.012"},{"key":"bibr7-0959651820945828","doi-asserted-by":"publisher","DOI":"10.1016\/j.ecolmodel.2015.06.016"},{"key":"bibr8-0959651820945828","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2006.05.101"},{"key":"bibr9-0959651820945828","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2019.04.007"},{"key":"bibr10-0959651820945828","doi-asserted-by":"publisher","DOI":"10.1007\/s00521-016-2641-9"},{"key":"bibr11-0959651820945828","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2017.12.046"},{"key":"bibr12-0959651820945828","doi-asserted-by":"publisher","DOI":"10.1007\/s11432-017-9448-8"},{"key":"bibr13-0959651820945828","doi-asserted-by":"publisher","DOI":"10.1109\/9.911430"},{"key":"bibr14-0959651820945828","doi-asserted-by":"publisher","DOI":"10.1049\/iet-cta.2015.0108"},{"key":"bibr15-0959651820945828","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfranklin.2016.06.033"},{"key":"bibr16-0959651820945828","doi-asserted-by":"publisher","DOI":"10.1515\/amcs-2017-0017"},{"key":"bibr17-0959651820945828","doi-asserted-by":"publisher","DOI":"10.1002\/acs.2852"},{"key":"bibr18-0959651820945828","doi-asserted-by":"publisher","DOI":"10.1137\/18M1224210"},{"key":"bibr19-0959651820945828","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-3800(00)00279-9"},{"key":"bibr20-0959651820945828","doi-asserted-by":"publisher","DOI":"10.1002\/9781118033029"},{"key":"bibr21-0959651820945828","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2010.10.019"},{"key":"bibr22-0959651820945828","doi-asserted-by":"publisher","DOI":"10.1137\/100812124"},{"key":"bibr23-0959651820945828","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2012.06.073"},{"key":"bibr24-0959651820945828","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2015.10.007"},{"key":"bibr25-0959651820945828","doi-asserted-by":"publisher","DOI":"10.1080\/00207179.2013.796526"},{"key":"bibr26-0959651820945828","volume-title":"10th international multi-conferences on systems, signals & devices 2013 (SSD13)","author":"Hamdi SE"},{"key":"bibr27-0959651820945828","volume-title":"Positive system, lecture notes in control and information sciences","author":"Cacace F","year":"2017"},{"key":"bibr28-0959651820945828","doi-asserted-by":"publisher","DOI":"10.1002\/asjc.1984"},{"key":"bibr29-0959651820945828","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2015.2504516"},{"key":"bibr30-0959651820945828","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-02894-6"},{"key":"bibr31-0959651820945828","volume-title":"IEEE vehicle power and propulsion conference (VPPC)","author":"Huong DC"}],"container-title":["Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/0959651820945828","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.1177\/0959651820945828","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/0959651820945828","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T22:39:38Z","timestamp":1777675178000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.1177\/0959651820945828"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,8,11]]},"references-count":31,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2021,4]]}},"alternative-id":["10.1177\/0959651820945828"],"URL":"https:\/\/doi.org\/10.1177\/0959651820945828","relation":{},"ISSN":["0959-6518","2041-3041"],"issn-type":[{"value":"0959-6518","type":"print"},{"value":"2041-3041","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,8,11]]}}}