This monograph studies the design of robust, monotonically convergent iterative learning controllers (ILC) for discrete-time systems. It takes account of the recently developed comprehensive approach to robust ILC analysis and design established to handle the situation where the plant model is uncertain. Considering ILC in the iteration domain, it presents a unified analysis and design framework that enables designers to consider both robustness and monotonic convergence for typical uncertainty models, including parametric interval uncertainties, iteration-domain frequency uncertainty, and iteration-domain stochastic uncertainty. It presents solutions to three fundamental robust interval computational problems (used as basic tools for designing robust ILC controllers): finding the maximum singular value of an interval matrix, determining the robust stability of interval polynomial matrix, and obtaining the power of an interval matrix.