In this paper a new robust control strategy for MIMO LTI plants is presented. The proposed approach results in an output feedback and the resulting control system exhibits strong robustness properties. The derivation of the control policy is based on the mathematical machinery of the Singular Perturbation Theory. More specifically, a high order sliding motion is imposed, and a suitable definition of a time-varying sliding manifold allows the controlled plant output to robustly track a prescribed reference trajectory. Simulations are presented considering a classic IFAC benchmark problem, namely a three-input-three-output binary distillation column with an unmatched disturbance and bounded control variables. The results of the simulation show the effectiveness of the proposed approach.