{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,7]],"date-time":"2025-11-07T13:29:22Z","timestamp":1762522162762},"reference-count":23,"publisher":"University of Zielona G\u00f3ra, Poland","issue":"1","license":[{"start":{"date-parts":[[2018,3,1]],"date-time":"2018-03-01T00:00:00Z","timestamp":1519862400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2018,3,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p> We consider the problem of joint estimation of states and some constant parameters for a class of nonlinear discrete-time systems. This class contains systems that could be transformed into a quasi-LPV (linear parameter varying) polytopic model in the Takagi-Sugeno (T-S) form. Such systems could have unmeasured premise variables, a case usually overlooked in the observer design literature. We assert that, for such systems in discrete-time, the current literature lacks design strategies for joint state and parameter estimation. To this end, we adapt the existing literature on continuous-time linear systems for joint state and time-varying parameter estimation. We first develop the discrete-time version of this result for linear systems. A Lyapunov approach is used to illustrate stability, and bounds for the estimation error are obtained via the bounded real lemma. We use this result to achieve our objective for a design procedure for a class of nonlinear systems with constant parameters. This results in less conservative conditions and a simplified design procedure. A basic waste water treatment plant simulation example is discussed to illustrate the design procedure.<\/jats:p>","DOI":"10.2478\/amcs-2018-0004","type":"journal-article","created":{"date-parts":[[2018,3,31]],"date-time":"2018-03-31T22:16:18Z","timestamp":1522534578000},"page":"55-67","source":"Crossref","is-referenced-by-count":7,"title":["An adaptive observer design approach for a class of discrete-time nonlinear systems"],"prefix":"10.61822","volume":"28","author":[{"given":"Krishnan","family":"Srinivasarengan","sequence":"first","affiliation":[{"name":"CRAN UMR 7039, CNRS University of Lorraine, F-54000 Vandoeuvre-l\u00e8s-Nancy , France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jos\u00e9","family":"Ragot","sequence":"additional","affiliation":[{"name":"CRAN UMR 7039, CNRS University of Lorraine, F-54000 Vandoeuvre-l\u00e8s-Nancy , France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Christophe","family":"Aubrun","sequence":"additional","affiliation":[{"name":"CRAN UMR 7039, CNRS University of Lorraine, F-54000 Vandoeuvre-l\u00e8s-Nancy , France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Didier","family":"Maquin","sequence":"additional","affiliation":[{"name":"CRAN UMR 7039, CNRS University of Lorraine, F-54000 Vandoeuvre-l\u00e8s-Nancy , France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"37438","published-online":{"date-parts":[[2018,3,31]]},"reference":[{"key":"2023050302340596105_j_amcs-2018-0004_ref_001_w2aab3b7b3b1b6b1ab1ab1Aa","doi-asserted-by":"crossref","unstructured":"Bezzaoucha, S., Marx, B., Maquin, D. and Ragot, J. 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