{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,22]],"date-time":"2025-11-22T11:05:33Z","timestamp":1763809533102,"version":"build-2065373602"},"reference-count":0,"publisher":"University of Zielona G\u00f3ra, Poland","issue":"3","license":[{"start":{"date-parts":[[2012,9,1]],"date-time":"2012-09-01T00:00:00Z","timestamp":1346457600000},"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":[[2012,9,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>This paper deals with the stability study of the nonlinear Saint-Venant Partial Differential Equation (PDE). The proposed approach is based on the multi-model concept which takes into account some Linear Time Invariant (LTI) models defined around a set of operating points. This method allows describing the dynamics of this nonlinear system in an infinite dimensional space over a wide operating range. A stability analysis of the nonlinear Saint-Venant PDE is proposed both by using Linear Matrix Inequalities (LMIs) and an Internal Model Boundary Control (IMBC) structure. The method is applied both in simulations and real experiments through a microchannel, illustrating thus the theoretical results developed in the paper.<\/jats:p>","DOI":"10.2478\/v10006-012-0041-6","type":"journal-article","created":{"date-parts":[[2016,3,3]],"date-time":"2016-03-03T11:05:27Z","timestamp":1457003127000},"page":"539-550","source":"Crossref","is-referenced-by-count":15,"title":["A multi-model approach to Saint-Venant equations: A stability study by LMIs"],"prefix":"10.61822","volume":"22","author":[{"given":"Val\u00e9rie","family":"Dos Santos Martins","sequence":"first","affiliation":[{"name":"Automatic and Process Control Laboratory (LAGEP) University of Lyon 1, CNRS, UMR 5007, Villeurbanne F-69622, France"}]},{"given":"Mickael","family":"Rodrigues","sequence":"additional","affiliation":[{"name":"Automatic and Process Control Laboratory (LAGEP) University of Lyon 1, CNRS, UMR 5007, Villeurbanne F-69622, France"}]},{"given":"Mamadou","family":"Diagne","sequence":"additional","affiliation":[{"name":"Automatic and Process Control Laboratory (LAGEP) University of Lyon 1, CNRS, UMR 5007, Villeurbanne F-69622, France"}]}],"member":"37438","published-online":{"date-parts":[[2012,9,28]]},"container-title":["International Journal of Applied Mathematics and Computer Science"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/content.sciendo.com\/view\/journals\/amcs\/22\/3\/article-p539.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.sciendo.com\/pdf\/10.2478\/v10006-012-0041-6","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,2,29]],"date-time":"2024-02-29T10:29:20Z","timestamp":1709202560000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.sciendo.com\/article\/10.2478\/v10006-012-0041-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,9,1]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2012,9,28]]},"published-print":{"date-parts":[[2012,9,1]]}},"alternative-id":["10.2478\/v10006-012-0041-6"],"URL":"https:\/\/doi.org\/10.2478\/v10006-012-0041-6","relation":{},"ISSN":["2083-8492"],"issn-type":[{"type":"electronic","value":"2083-8492"}],"subject":[],"published":{"date-parts":[[2012,9,1]]}}}