We propose a robust self-triggered control algorithm for constrained linear discrete-time systems subject to additive disturbances based on MPC. At every sampling instant, the controller provides both the next sampling instant, as well as the inputs that are applied to the system until the next sampling instant. By maximizing the inter-sampling time subject to bounds on the MPC value function, the average sampling frequency in the closed-loop system is decreased while guaranteeing an upper bound on the performance loss when compared with an MPC scheme sampling at every point in time. Robust constraint satisfaction is achieved by tightening input and state constraints based on a Tube MPC approach. Moreover, a compact set in the state space, which is a parameter in the MPC scheme, is shown to be robustly asymptotically stabilized. (C) 2016 Elsevier Ltd. All rights reserved.