Abstract: A robust low complexity model predictive control(MPC) scheme,referred to as robust one-step control,is proposed for a class of constrained discrete-time piecewise affine(PWA) systems with bounded additive disturbance.First, based on the maximal robust positively invariant set,the maximal robust stabilizable set is computed and chosen as the constraint set of the first predicted state in MPC formulation,such that the resulting receding horizon(RH) controller can control maximal robust stabilizable set with shorter prediction horizons.Second,the robust stability is analyzed via linear matrix inequalities(LMIs) outside of maximal robust positively invariant set.The combination of these two components guarantees the robust feasibility of the controller and stability of closed-loop system.Extensive numerical examples show that the controller with lower complexity can be obtained with one-step control scheme compared with existing ones.