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A non-fragile observer is proposed to estimate the system states, and an observer-based adaptive sliding mode controller is synthesized to ensure the reachability of the sliding surfaces in the state-estimation space in finite time. The sufficient condition for stochastic stability of the error system and sliding mode dynamics is derived in the form of linear matrix inequalities (LMIs). Finally, some numerical examples are presented to illustrate the effectiveness of the proposed method. <\/jats:p>","DOI":"10.1177\/0142331219891590","type":"journal-article","created":{"date-parts":[[2020,1,6]],"date-time":"2020-01-06T10:52:18Z","timestamp":1578307938000},"page":"1448-1460","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":12,"title":["A non-fragile observer-based adaptive sliding mode control for fractional-order Markovian jump systems with time delay and input nonlinearity"],"prefix":"10.1177","volume":"42","author":[{"given":"Majid","family":"Parvizian","sequence":"first","affiliation":[{"name":"Intelligent Control Systems Laboratory, School of Electrical and Computer Engineering, Tarbiat Modares University, Iran"}]},{"given":"Khosro","family":"Khandani","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, Faculty of Engineering, Arak University, Iran"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0916-842X","authenticated-orcid":false,"given":"Vahid Johari","family":"Majd","sequence":"additional","affiliation":[{"name":"Intelligent Control Systems Laboratory, School of Electrical and Computer Engineering, Tarbiat Modares University, Iran"}]}],"member":"179","published-online":{"date-parts":[[2020,1,6]]},"reference":[{"key":"bibr1-0142331219891590","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2018.09.035"},{"key":"bibr2-0142331219891590","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2017.04.035"},{"key":"bibr3-0142331219891590","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2016.08.027"},{"key":"bibr4-0142331219891590","doi-asserted-by":"publisher","DOI":"10.1016\/j.sigpro.2012.02.009"},{"key":"bibr5-0142331219891590","volume-title":"Stochastic Switching Systems: Analysis and Design","author":"Boukas EK","year":"2007"},{"key":"bibr6-0142331219891590","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611970777"},{"key":"bibr7-0142331219891590","doi-asserted-by":"publisher","DOI":"10.1002\/oca.931"},{"key":"bibr8-0142331219891590","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2013.02.014"},{"key":"bibr9-0142331219891590","doi-asserted-by":"publisher","DOI":"10.1109\/CDC.2011.6161100"},{"key":"bibr10-0142331219891590","doi-asserted-by":"publisher","DOI":"10.1016\/j.isatra.2016.02.015"},{"key":"bibr11-0142331219891590","doi-asserted-by":"publisher","DOI":"10.1016\/j.ymssp.2017.11.010"},{"key":"bibr12-0142331219891590","doi-asserted-by":"publisher","DOI":"10.1080\/00207179.2016.1210235"},{"key":"bibr13-0142331219891590","doi-asserted-by":"publisher","DOI":"10.1049\/iet-cta.2010.0222"},{"key":"bibr14-0142331219891590","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2013.12.012"},{"key":"bibr15-0142331219891590","doi-asserted-by":"publisher","DOI":"10.1177\/0142331217744486"},{"key":"bibr16-0142331219891590","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2018.10.054"},{"key":"bibr17-0142331219891590","doi-asserted-by":"publisher","DOI":"10.1002\/rnc.2970"},{"key":"bibr18-0142331219891590","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2016.2594261"},{"key":"bibr19-0142331219891590","doi-asserted-by":"publisher","DOI":"10.1080\/00207721.2016.1216201"},{"key":"bibr20-0142331219891590","doi-asserted-by":"publisher","DOI":"10.1080\/00207179.2012.723138"},{"key":"bibr21-0142331219891590","doi-asserted-by":"publisher","DOI":"10.1016\/j.sysconle.2013.09.007"},{"key":"bibr22-0142331219891590","doi-asserted-by":"publisher","DOI":"10.1007\/s11633-013-0724-y"},{"key":"bibr23-0142331219891590","doi-asserted-by":"publisher","DOI":"10.1093\/imamci\/dns012"},{"key":"bibr24-0142331219891590","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2015.11.007"},{"key":"bibr25-0142331219891590","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2009.04.003"},{"key":"bibr26-0142331219891590","doi-asserted-by":"publisher","DOI":"10.1080\/00207179.2016.1272716"},{"key":"bibr27-0142331219891590","doi-asserted-by":"publisher","DOI":"10.1002\/asjc.1391"},{"key":"bibr28-0142331219891590","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2018.09.028"},{"key":"bibr29-0142331219891590","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2009.07.027"},{"key":"bibr30-0142331219891590","volume-title":"Jump Linear Systems in Automatic Control","author":"Mariton M","year":"1990"},{"key":"bibr31-0142331219891590","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2009.05.004"},{"key":"bibr32-0142331219891590","doi-asserted-by":"crossref","unstructured":"Montseny G (1998) Diffusive representation of pseudo-differential time-operators. 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