{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,6]],"date-time":"2026-06-06T01:00:02Z","timestamp":1780707602203,"version":"3.54.1"},"reference-count":31,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2022,10,13]],"date-time":"2022-10-13T00:00:00Z","timestamp":1665619200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Norwegian University of Science and Technology","award":["22-29-01303"],"award-info":[{"award-number":["22-29-01303"]}]},{"name":"Russian Scientific Foundation","award":["22-29-01303"],"award-info":[{"award-number":["22-29-01303"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, we consider the problem involved when designing the interval observer for the system described by a linear discrete-time model under external disturbances and measurement noises. To solve this problem, we used the reduced order model of the initial system, which is insensitive or has minimal sensitivity to the disturbances. The relations involved in designing the interval observer, which has minimal dimensions and estimates the prescribed linear function of the original system state vector, were obtained. The theoretical results were illustrated by a practical example.<\/jats:p>","DOI":"10.3390\/sym14102131","type":"journal-article","created":{"date-parts":[[2022,10,14]],"date-time":"2022-10-14T01:44:13Z","timestamp":1665711853000},"page":"2131","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Interval Observers for Discrete-Time Linear Systems with Uncertainties"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4270-6872","authenticated-orcid":false,"given":"Oleg","family":"Sergiyenko","sequence":"first","affiliation":[{"name":"Engineering Institute, Universidad Autonoma de Baja California, Mexicali 21280, Mexico"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5927-7117","authenticated-orcid":false,"given":"Alexey","family":"Zhirabok","sequence":"additional","affiliation":[{"name":"Department of Automation and Robotics, Far Eastern Federal University, 690990 Vladivostok, Russia"},{"name":"Institute of Marine Technology Problems, 690990 Vladivostok, Russia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7009-3634","authenticated-orcid":false,"given":"Ibraheem Kasim","family":"Ibraheem","sequence":"additional","affiliation":[{"name":"Computer Engineering Techniques Department, Al-Mustaqbal University College, Hilla 51001, Iraq"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Alexander","family":"Zuev","sequence":"additional","affiliation":[{"name":"Department of Automation and Robotics, Far Eastern Federal University, 690990 Vladivostok, Russia"},{"name":"Institute of Marine Technology Problems, 690990 Vladivostok, Russia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Vladimir","family":"Filaretov","sequence":"additional","affiliation":[{"name":"Department of Automation and Robotics, Far Eastern Federal University, 690990 Vladivostok, Russia"},{"name":"Institute of Automation and Control Processes, 690041 Vladivostok, Russia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7869-6373","authenticated-orcid":false,"given":"Ahmad Taher","family":"Azar","sequence":"additional","affiliation":[{"name":"College of Computer and Information Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia"},{"name":"Faculty of Computers and Artificial Intelligence, Benha University, Benha 13518, Egypt"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1252-260X","authenticated-orcid":false,"given":"Ibrahim A.","family":"Hameed","sequence":"additional","affiliation":[{"name":"Department of ICT and Natural Sciences, Norwegian University of Science and Technology, Larsgardsvegen, 2, 6009 Alesund, Norway"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,10,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"541","DOI":"10.1016\/S0005-1098(99)00177-6","article-title":"Sliding mode observers for fault detection and isolation","volume":"36","author":"Edwards","year":"2000","journal-title":"Automatica"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"773","DOI":"10.1080\/00207720701409538","article-title":"Observation of linear systems with unknown inputs via high-order sliding-modes","volume":"38","author":"Fridman","year":"2007","journal-title":"Int. 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