{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,4]],"date-time":"2026-05-04T20:44:07Z","timestamp":1777927447264,"version":"3.51.4"},"reference-count":32,"publisher":"SAGE Publications","issue":"10","license":[{"start":{"date-parts":[[2023,6,14]],"date-time":"2023-06-14T00:00:00Z","timestamp":1686700800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"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":[[2023,11]]},"abstract":"<jats:p>This article deals with the observability bound problem of a discrete-time nonlinear singularly perturbed systems (SPSs) subject to disturbances and noises. This nonlinear SPS is represented by a coupled state multimodel (MM) with unmeasurable premise variables. A [Formula: see text] proportional-integral multiobserver ([Formula: see text] PI multiobserver), known by its robustness, is designed to accomplish this task. The proposed method is based on the [Formula: see text] technique to minimize the effect of the disturbances, the noises, and all the unmeasurable premise variables. To design this observer, sufficient conditions expressed in terms of linear matrix inequalities (LMIs) are developed as a first step to ensure the robust stability bound of the considered system represented by a coupled MM for a bound of the singular perturbation parameter based on a quadratic Lyapunov function and the [Formula: see text] gain. Then, sufficient conditions are developed to ensure the robust stability bound of the state estimation error between the MM and the PI multiobserver for a bound of the singular perturbation parameter that is less than or equal to the considered system\u2019s robust stability bound. Hence, the observability bound of the considered system represented by a coupled state MM is determined. Two simulation examples are then given to validate the proposed strategy.<\/jats:p>","DOI":"10.1177\/09596518231173769","type":"journal-article","created":{"date-parts":[[2023,6,14]],"date-time":"2023-06-14T03:04:41Z","timestamp":1686711881000},"page":"1719-1736","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":1,"title":["Robust PI multiobserver for discrete nonlinear singularly perturbed system with unmeasurable premise variables"],"prefix":"10.1177","volume":"237","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0281-5935","authenticated-orcid":false,"given":"Ltifi","family":"Marwa","sequence":"first","affiliation":[{"name":"Laboratory: Numerical Control of Industrial Processes (CONPRI), Department of Electrical Engineering, National Engineering School of Gabes, University of Gabes, Gabes, Tunisia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bahri","family":"Nesrine","sequence":"additional","affiliation":[{"name":"Laboratory: Numerical Control of Industrial Processes (CONPRI), Department of Electrical Engineering, National Engineering School of Gabes, University of Gabes, Gabes, Tunisia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ltaief","family":"Majda","sequence":"additional","affiliation":[{"name":"Laboratory: Numerical Control of Industrial Processes (CONPRI), Department of Electrical Engineering, National Engineering School of Gabes, University of Gabes, Gabes, Tunisia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2023,6,14]]},"reference":[{"key":"bibr1-09596518231173769","doi-asserted-by":"publisher","DOI":"10.1007\/s00202-016-0507-x"},{"key":"bibr2-09596518231173769","doi-asserted-by":"publisher","DOI":"10.1007\/s00202-007-0085-z"},{"key":"bibr3-09596518231173769","doi-asserted-by":"publisher","DOI":"10.1023\/A:1017943816350"},{"key":"bibr4-09596518231173769","doi-asserted-by":"publisher","DOI":"10.1115\/1.4048933"},{"key":"bibr5-09596518231173769","doi-asserted-by":"publisher","DOI":"10.1002\/rnc.1593"},{"issue":"1","key":"bibr6-09596518231173769","first-page":"19","volume":"12","author":"Aliyu MDS","year":"2012","journal-title":"Nonlin Dyn Syst Theor"},{"key":"bibr7-09596518231173769","doi-asserted-by":"publisher","DOI":"10.1109\/TCSI.2011.2106031"},{"key":"bibr8-09596518231173769","first-page":"1047","volume-title":"Proceedings of the 53rd IEEE conference on decision and control","author":"Najmeh D"},{"key":"bibr9-09596518231173769","doi-asserted-by":"publisher","DOI":"10.1002\/rnc.5100"},{"key":"bibr10-09596518231173769","first-page":"2165","volume-title":"Proceedings of the 41st IEEE conference on decision and control","volume":"2","author":"Assawinchaichote W"},{"key":"bibr11-09596518231173769","doi-asserted-by":"publisher","DOI":"10.1109\/TSMCB.2008.927277"},{"key":"bibr12-09596518231173769","doi-asserted-by":"publisher","DOI":"10.1109\/TSP.2004.827182"},{"key":"bibr13-09596518231173769","doi-asserted-by":"publisher","DOI":"10.1021\/ie8017687"},{"key":"bibr14-09596518231173769","doi-asserted-by":"publisher","DOI":"10.3182\/20080706-5-KR-1001.00466"},{"key":"bibr15-09596518231173769","first-page":"5718","volume-title":"Proceedings of the 2015 American control conference (ACC)","author":"Nagy-Kiss AM"},{"key":"bibr16-09596518231173769","doi-asserted-by":"publisher","DOI":"10.1016\/j.jprocont.2013.09.027"},{"key":"bibr17-09596518231173769","first-page":"579","volume-title":"Proceedings of the 2016 3rd conference on control and fault-tolerant systems (SysTol)","author":"Mart\u00ednez-Garc\u00eda C"},{"key":"bibr18-09596518231173769","doi-asserted-by":"publisher","DOI":"10.1504\/IJMIC.2012.051086"},{"key":"bibr19-09596518231173769","doi-asserted-by":"publisher","DOI":"10.1007\/s11633-014-0815-4"},{"key":"bibr20-09596518231173769","doi-asserted-by":"publisher","DOI":"10.1016\/j.jprocont.2022.06.009"},{"key":"bibr21-09596518231173769","doi-asserted-by":"publisher","DOI":"10.1016\/j.egypro.2019.04.021"},{"key":"bibr22-09596518231173769","first-page":"1","volume-title":"Proceedings of the 2017 25th Mediterranean conference on control and automation (MED)","author":"Asma BR"},{"key":"bibr23-09596518231173769","first-page":"95","volume-title":"Proceedings of the 2021 IEEE 2nd international conference on signal, control and communication (SCC)","author":"Rajab AB"},{"key":"bibr24-09596518231173769","first-page":"3577","volume-title":"Proceedings of the 2008 47th IEEE conference on decision and control","author":"Orjuela R"},{"key":"bibr25-09596518231173769","first-page":"353","volume-title":"Proceedings of the 2009 17th Mediterranean conference on control and automation","author":"Ichalal D"},{"key":"bibr26-09596518231173769","doi-asserted-by":"publisher","DOI":"10.1080\/00207721.2014.884252"},{"key":"bibr27-09596518231173769","doi-asserted-by":"crossref","unstructured":"Ilham H, Mohamed E, Abdellatif EA, et al. Observer design for a class of discrete-time Takagi-Sugeno models with unmeasurable premise variables: application to an asynchronous motor. 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