This paper proposes a new MPC control scheme for polytopic uncertain and/or time-varying systems with state and input constraints. The MPC policies we consider employ: i) the intersection of ellipsoids to characterize the domain of attraction, ii) a time-varying Lyapunov function to bound from above the cost function, iii) a tailored ADMM algorithm to solve efficiently the online optimization problem. With respect to other well known techniques, the main advantage of the new approach is the reduced conservativeness.