This paper studies the robust convergence properties of iterative learning control (ILC) for single-input, single-output (SISO), nonrepetitive systems subject to iteration-dependent uncertainties that arise in not only initial states and external disturbances but also plant models. Given an extended relative degree condition, it is possible to propose necessary and sufficient (NAS) conditions for robust ILC convergence. The tracking error bound is shown to depend continuously on the bounds of the iteration-dependent uncertainties. When the iteration-dependent uncertainties are bounded, NAS conditions exist to guarantee bounded system trajectories and output tracking error. If the iteration-dependent uncertainties converge, then NAS conditions ensure bounded system trajectories and zero output tracking error. The results are also extended to a class of affine nonlinear systems satisfying a Lipschitz condition. Simulation tests on a representative batch process demonstrate the validity of the obtained robust ILC convergence results. (C) 2017 Elsevier Ltd. All rights reserved.