The paper presents a generalized algorithm for the reaching and boundedness of the sliding variable in case of discrete time sliding mode control systems. The algorithm is general as it not only comprises functions in the sliding variable, but also functions in other variables, which are known. With the help of the proposed generalized reaching law, an important problem of a reaching law with uncertainty bounded by known functions is studied. The convergence of the sliding variable to an ultimate bounding function in presence of such an uncertainty is shown by the band approach method. This is achieved by appropriately selecting the functions in the proposed generalized reaching law. (C) 2014 Elsevier Ltd. All rights reserved.