Traditionally, the convergence rate of the sliding variable given by a discrete reaching law has been fixed in nature. This paper presents a generalized algorithm for discrete time sliding mode control systems which offers a flexible convergence rate for the sliding variable. For analysis, we use the recently developed band approach method which gives us the values of the parameters in the algorithm for the desired convergence to take place, once the ultimate band is chosen appropriately. (C) 2015 Elsevier Ltd. All rights reserved.