In this paper, we present a novel Robust Monotonic Convergence (RMC) analysis approach for finite time interval Iterative Learning Control (ILC) for uncertain systems. For that purpose, a finite time interval model for uncertain systems is introduced. This model is subsequently used in an RMC analysis based on mu analysis. As a result, we can handle additive and multiplicative uncertainty models in the RMC problem formulation, analyze RMC of linear time invariant MIMO systems controlled by any linear trial invariant ILC controller, and formulate additional straightforward RMC conditions for ILC controlled systems. To illustrate the derived results, we analyze the RMC properties of linear quadratic (LQ) norm optimal ILC. (C) 2009 Elsevier Ltd. All rights reserved.