Monotonically convergent ILC systems designed using bounded real lemma

This article is devoted to iterative learning control (ILC) systems design for multiple-input multiple-output (MIMO), linear time-invariant (LTI) plants. With the bounded real lemma (BRL) applied, a linear matrix inequality (LMI) design approach is presented to develop sufficient conditions for the monotonic convergence of the ILC process. It is shown that regardless of a system relative degree, the convergence conditions can be expressed in terms of LMIs, and formulas can be derived for the learning gain matrices design. For ILC determined in this way, two illustrative examples are provided to verify its effectiveness and robustness against structured and polytopic-type uncertainties.