This paper deals with the problem of stabilizing n integrators in cascade with bounded input using a discrete-time controller. We propose here a control algorithm using saturation functions for the case of 3 integrators and then we extend the development to the case of n integrators. The control methodology developed is simple and is explicitly given. We also present a discrete-time algorithm to control n integrators with a bounded input including a delay and we design an observer by considering that we only measure the output of the integrators chain. We present a real-time application of the proposed control algorithm for the stabilization of the orientation of a mini-rotorcraft.