Initial shift problem for robust iterative learning control systems with polytopic-type uncertainty

This article deals with the initial shift problem of robust iterative learning control (ILC) for uncertain continuous-time systems. Two ILC laws are considered by the two-dimensional (2-D) analysis approach. It is shown that a necessary and sufficient convergence condition can be directly derived using the theory of 2-D systems. It is also shown that if the system parameters are subject to polytopic-type uncertainties, this convergence condition can induce a sufficient condition for the robust ILC convergence. Furthermore, the 2-D analysis approach can be extended to address the initial shift problem of robust ILC for multiple-input-multiple-output, uncertain time-delay systems. Two numerical simulation examples are provided to illustrate the theoretical results.