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In this paper, an observer design for systems with distributed parameters using sliding modes theory and backstepping-like procedure in order to achieve exponential convergence is presented. Such an observer is built using the knowledge available within and throughout an integral transformation of Volterra with the output injection functions. The gains of the observer, which are attained by solving a partial differential equations system with output injection, will guarantee the exponential convergence of the observer. The design method is applied to an epidemic system to consider the sensitive population S.<\/jats:p>","DOI":"10.1177\/0142331216661621","type":"journal-article","created":{"date-parts":[[2016,8,25]],"date-time":"2016-08-25T22:29:39Z","timestamp":1472164179000},"page":"542-549","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":5,"title":["Backstepping and sliding modes for observer design of distributed parameter system"],"prefix":"10.1177","volume":"40","author":[{"given":"Abdessamad","family":"Abdelhedi","sequence":"first","affiliation":[{"name":"National Engineering School Of Gabes, Zrig 6029, Gabes,Tunisia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wided","family":"Saadi","sequence":"additional","affiliation":[{"name":"National Engineering School Of Gabes, Zrig 6029, Gabes,Tunisia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Driss","family":"Boutat","sequence":"additional","affiliation":[{"name":"INSA Centre Val de Loire, Orlans university, 18022 Bourges, French"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lasaad","family":"Sbita","sequence":"additional","affiliation":[{"name":"National Engineering School Of Gabes, Zrig 6029, Gabes,Tunisia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2016,8,25]]},"reference":[{"key":"bibr1-0142331216661621","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-6911(03)00222-6"},{"key":"bibr2-0142331216661621","doi-asserted-by":"publisher","DOI":"10.1002\/rnc.1225"},{"key":"bibr3-0142331216661621","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2010.01.028"},{"key":"bibr4-0142331216661621","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0006761"},{"key":"bibr5-0142331216661621","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2005.858636"},{"key":"bibr6-0142331216661621","doi-asserted-by":"publisher","DOI":"10.1109\/ROSE.2011.6058523"},{"key":"bibr7-0142331216661621","doi-asserted-by":"publisher","DOI":"10.1109\/ACC.2006.1655449"},{"key":"bibr8-0142331216661621","doi-asserted-by":"publisher","DOI":"10.23919\/ECC.2013.6669752"},{"key":"bibr9-0142331216661621","doi-asserted-by":"publisher","DOI":"10.1109\/ACC.2006.1656581"},{"key":"bibr10-0142331216661621","doi-asserted-by":"publisher","DOI":"10.1016\/j.sysconle.2008.02.005"},{"key":"bibr11-0142331216661621","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898718607"},{"key":"bibr12-0142331216661621","first-page":"215","volume-title":"Encyclopedia of Mathematics and its Applications","volume":"74","author":"Lasiecka I","year":"2000"},{"key":"bibr13-0142331216661621","volume-title":"3\u00e8mes Journ\u00e9es Doctorales\/Journ\u00e9es Nationales MACS","author":"Li XD","year":"2009"},{"key":"bibr14-0142331216661621","doi-asserted-by":"publisher","DOI":"10.1109\/VSS.2010.5544678"},{"key":"bibr15-0142331216661621","unstructured":"Orlov Y (2009) Discontinuous Systems: Lyapunov Analysis and Robust Synthesis under Uncertainty Conditions. 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