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In this study, an equivalent standard state-space system (ESSS) with fault and unknown disturbances is firstly obtained for the considered descriptor stochastic system, and then a recursive filter is designed based on the ESSS representation. Moreover, this study proposes a recursive filter design method to deal with the effect of the unknown disturbances. The relationship between the proposed filter and the existing results in the literature is addressed. Finally, an illustrative example is given to illustrate the effectiveness of the recursive five-step state and fault estimator.<\/jats:p>","DOI":"10.1142\/s0218126618500834","type":"journal-article","created":{"date-parts":[[2017,9,29]],"date-time":"2017-09-29T03:29:34Z","timestamp":1506655774000},"page":"1850083","source":"Crossref","is-referenced-by-count":10,"title":["Recursive Five-Step Filter for State and Fault Estimation of Linear Descriptor Stochastic Systems with Unknown Disturbances"],"prefix":"10.1142","volume":"27","author":[{"given":"Talel","family":"Bessaoudi","sequence":"first","affiliation":[{"name":"Laboratory of Engineering of Industrial Systems and Renewable Energy (LISIER), National Higher Engineering School of Tunis (ENSIT), University of Tunis, 5 Avenue Taha Hussein, BP 56 - 1008 Tunis, Tunisia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fay\u00e7al","family":"Ben Hmida","sequence":"additional","affiliation":[{"name":"Laboratory of Engineering of Industrial Systems and Renewable Energy (LISIER), National Higher Engineering School of Tunis (ENSIT), University of Tunis, 5 Avenue Taha Hussein, BP 56 - 1008 Tunis, Tunisia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2018,2,22]]},"reference":[{"key":"S0218126618500834BIB001","doi-asserted-by":"publisher","DOI":"10.1049\/iet-cta.2014.0641"},{"key":"S0218126618500834BIB002","doi-asserted-by":"publisher","DOI":"10.1155\/2015\/867206"},{"key":"S0218126618500834BIB003","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfranklin.2012.05.004"},{"key":"S0218126618500834BIB004","doi-asserted-by":"publisher","DOI":"10.2478\/v10006-011-0049-3"},{"key":"S0218126618500834BIB005","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfranklin.2011.04.005"},{"key":"S0218126618500834BIB006","doi-asserted-by":"crossref","first-page":"343586","DOI":"10.1155\/2010\/343586","volume":"2010","author":"Ben Hmida F.","year":"2010","journal-title":"Math. 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