This paper discusses the robustness of a plant-inversion based Switched Iterative Learning Control (SILC) scheme for a special class of multivariable systems where measurement access is limited to one output channel at any time. Previous work has shown that it is impossible for such systems to achieve zero error convergence with standard Iterative Learning Control (ILC), however, possible with SILC for appropriately designed learning matrix. The most intuitive and convenient approach to construct such a learning matrix is to directly invert the plant dynamics. Although this approach perfectly decouples the nominal plant dynamics and, thus, automatically satisfies the convergence conditions, its effectiveness when the system is contaminated with uncertainty is not examined. This work investigates the degree of robustness of this plant-inversion design to multiplicative unstructured uncertainties. The result demonstrates to what extent to which the robustness of the proposed approach is achieved.