This paper presents a plant-inversion based Switched Iterative Learning Control (SILC) scheme for a special class of Multi-Input Multi-Output (MIMO) systems for which only one output channel can be accessed at any given time. While Asymptotic Stability (AS), or zero error convergence, is predominantly considered in Iterative Learning Control (ILC), AS cannot be achieved for this class of systems. A weaker condition, bounded convergence, however, can be obtained. With the SILC scheme proposed in this paper, the measurement channels are accessed one at a time in a specific order. Each time an output channel is accessed, bounded convergence of all of the channel errors is achieved by using an ILC algorithm. As the access is switched from one channel to the next, the previously achieved convergent error is brought to a new value due to the change of measurement information, which may or may not be less than the previous one, depending on the structure of the learning matrix. Using the inverse plant dynamics as a learning matrix and as the switching action continues occurring, the bounded convergence tends to zero convergence. Illustrative examples are provided to demonstrate the effectiveness of the proposed SILC scheme and its robustness to modeling uncertainty.