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It is proved that an appropriate choice of the trajectory generator parameters ensures the existence of the quasi-sliding motion of the system according to the definition by Gao <jats:italic>et al.<\/jats:italic> (1995) in spite of the influence of disturbances. Moreover, the paper shows that the application of the desired trajectory based reaching law results in a significant reduction in the quasi-sliding mode band width and errors of all state variables. Therefore, in comparison with Gao\u2019s control method, the system\u2019s robustness is increased. The paper also presents an additional modification of the reaching law, which guarantees a further reduction in the quasi-sliding mode band in the case of slowly varying disturbances. The results are confirmed with a simulation example.<\/jats:p>","DOI":"10.2478\/amcs-2019-0038","type":"journal-article","created":{"date-parts":[[2019,10,1]],"date-time":"2019-10-01T02:52:53Z","timestamp":1569898373000},"page":"517-525","source":"Crossref","is-referenced-by-count":7,"title":["A Reference Trajectory Based Discrete Time Sliding Mode Control Strategy"],"prefix":"10.61822","volume":"29","author":[{"given":"Andrzej","family":"Bartoszewicz","sequence":"first","affiliation":[{"name":"Institute of Automatic Control , \u0141\u00f3d\u017a University of Technology , Stefanowskiego 18\/22, 90-924 \u0141\u00f3d\u017a , Poland"}]},{"given":"Katarzyna","family":"Adamiak","sequence":"additional","affiliation":[{"name":"Institute of Automatic Control , \u0141\u00f3d\u017a University of Technology , Stefanowskiego 18\/22, 90-924 \u0141\u00f3d\u017a , Poland"}]}],"member":"37438","published-online":{"date-parts":[[2019,9,28]]},"reference":[{"key":"2023050302354277746_j_amcs-2019-0038_ref_001_w2aab3b7b7b1b6b1ab1ab1Aa","doi-asserted-by":"crossref","unstructured":"Bartolini, G., Ferrara, A. and Usai, E. 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