In this study, a new algorithm for explicit model predictive control of linear discrete-time systems subject to linear constraints, disturbances, uncertainties, and actuator faults is developed. The algorithm is based on dynamic programming, constraint rearrangement, multi-parametric programming, and a solution combination procedure. First of all, the dynamic programming is used to recast the problem as a multi-stage optimization problem. Afterwards, the constraints are rearranged in an innovative manner to take into account the worst admissible situation of unknown bounded disturbances, uncertainties, and actuator faults. Then, the explicit solution of the reformulated optimization problem for each stage is obtained using the multi-parametric programming approaches. Finally, a recursive procedure for combination and substitution of the solutions is presented to extract the desired explicit control law. © 2018 Elsevier Ltd