Robust design of a class of time-delay iterative learning control systems with initial shifts

This paper is mainly devoted to the iterative learning control (ILC) design for time-delay systems (TDS) in the presence of initial shifts, especially when the system parameters are subject to polytopic-type uncertainties. The ILC laws using a pure error term and/or an initial rectifying action to address the initial shifts are considered, and the two-dimensional (2-D) system theory is employed to develop necessary and sufficient conditions for the asymptotic stability of ILC. For the monotonic convergence of ILC, sufficient conditions are presented in terms of linear matrix inequalities (LMIs) based on the bounded real lemma (BRL). It is shown that adding the pure error term in the D-type learning law helps to meet certain LMIs to achieve a monotonically convergent ILC law. Specifically, this property is first investigated for linear time-invariant systems (LTIS), which is then discussed for the possible extension to TDS. Two numerical examples are included to illustrate the main results.