In Iterative Learning Control design, convergence speed along the iteration domain is one of the most important performance factors. In this paper, we aim at achieving fastest convergence speed (time-optimal) for a variety of nonlinear non-affine Single-Input-Single-Output (SISO) plants, and focus on the family of the linear type iterative learning controllers, including first-order ILC and higher-order ILC. The control objective can be formulated as a kind of robust optimization: optimizing the worst case performance in the presence of the interval uncertainties. To quantify convergence speed, a learning performance index – Q-factor – is employed. The optimal learning gain is then obtained by solving a Min-max problem. From the robust optimal design, we also reach the following conclusion: under the same interval uncertainty and applying the same min-max design which is robust and optimal, the Q-factor of ILC sequences of lower order ILC is always less than that of higher order ILC in terms of time-weighted norm. In the sequel, the first order ILC achieves the fastest convergence speed in the iteration domain.