In this paper, the problem of controlling the stator currents in Doubly-Fed Induction Machines is considered under large symmetric and asymmetric variations of the line voltage. This point is crucial to use profitably such kind of machines in electric power generation by wind turbines, since their stator windings are connected directly to the line grid, and only the rotor ones are supplied by controlled voltage-source converters. Taking the cue from the issues affecting standard feedback linearizing solutions, an output controller is considered and a suitable trajectory planning is proposed for the marginally stable zero-dynamics. This allows preventing large oscillations in rotor fluxes and command voltages, usually triggered by line voltage variations. Simulations show the effectiveness of the proposed approach.