A robust PI based indirect-type iterative learning control (ILC) is proposed in this paper for industrial batch processes with time-varying uncertainties, based on a two-dimensional (2D) Fornasini-Marchesini (FM) model description of the batch process dynamics. An important merit is that the proposed ILC design is independent of the PI tuning in the closed-loop system, owing to that the ILC updating law is only implemented through tuning the set-point of the closed-loop system. By introducing a specified pole location of the closed-loop system, a robust PI controller design is firstly given with the H infinity performance index to maintain the closed-loop robust stability.Then by developing a 2D FM description of the batch operation with the designed PI controller, the control objective of minimizing the tracking error along both the time and batch directions is formulated based on the 2D robust H infinity control theory, such that a robust ILC updating law is determined by solving the linear matrix inequality (LMI) conditions established for holding the 2D system stability. Moreover, the batch-direction convergence rate can be separately tuned via the performance index in the above LMI conditions. An illustrative application to batch injection molding is given to demonstrate the effectiveness and merit of the proposed method. (C) 2019 Elsevier Ltd. All rights reserved.