This paper considers the robustness of an inverse iterative learning control algorithm. A simple learning gain results in robust convergence that is monotonic in the least squares sense provided that the multiplicative plant uncertainty satisfies a matrix positivity requirement. The results are extended to the frequency domain using a simple graphical Nyquist test. The analysis extends naturally to a parameter-optimal control setting. Non-monotone convergence is considered by using a simple weighted norm based on exponential weighting of time series.