A Q, L Factorization of Norm-Optimal Iterative Learning Control

In this paper we consider the Norm-Optimal Iterative Learning Control (ILC) problem for discrete-time linear multi-input, multi-output systems. The solution to this problem is well known and naturally factors into a form with a filter on the previous control, Lu and a filter on the previous error, L-e. We show that this solution can always be factored into a Q, L form where Q filters the previous control and QL filters the previous error. This latter form is popularized with frequency domain ILC designs, and this common factorization suggests some general relationships between Norm-Optimal and frequency domain design, which are explored. Although the Q, L factorization is well known for some special cases, the results here are general and include differently dimensioned control and observation windows.