Counterexample to iterative learning control of linear discrete-time multivariable systems (Q1962016)

It is a very interesting example of a rare recent scientific discussion. In IEEE Trans. Autom. Control 38, No. 1, 121-125 (1993; Zbl 0773.93019), \textit{J. E. Kurek} and \textit{L. Zaremba} developed the so-called extended iterative learning control (EILC) algorithm for discrete systems based on a 2D approach. In Automatica 34, No. 11, 1459-1462 (1998), \textit{Y. Fang} and \textit{T. W. S. Chow} modified this approach claiming also that the EILC fails in guaranteeing convergence. In this note, the author shows that this modification can fail for uncertain systems and proves that convergence of the EILC is guaranteed. In turn, Fang and Chow try in their reply (p. 329) to defend their approach.