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Robust gradient iterative learning control: time and frequency domain conditions

This paper considers the use of matrix models and the robustness of a gradient-based iterative learning control (ILC) algorithm using fixed learning gains to ensure monotonic convergence with respect to the mean square value (Euclidean norm) of the error time series. The paper provides a complete and rigorous analysis for the systematic use of matrix models in ILC. They provide necessary and sufficient conditions for robust monotonic convergence and permit the construction of sufficient frequency domain conditions for robust monotonic convergence on finite time intervals for both causal and non-causal controller dynamics.