In this paper a quasi-infinite horizon 1-norm GPC is presented. This controller. combined with a global uncertainty description and an uncertainty band-updating procedure, has led to a robust algorithm with extremely low computational requirements. Only a linear programming (LP) problem needs to be solved to compute a control profile. This scheme can be successfully applied even to hard non-linear systems with relatively fast dynamics, as the large computational burden related to non-linear model predictive controllers is avoided. Simulation results performed on several constrained non-linear systems are provided.