Direct and Indirect Technique Routes of Convergence Analysis for Discrete-time Iterative Learning Control

This note is concerned with the direct and indirect technique routes of convergence analysis for discrete-time iterative learning control. It is first illustrated that the direct and indirect technique routes of convergence analysis for iterative learning control do not cause any contradiction. Then, it is shown that in the case the input-output coupling matrix is full-row rank, with resort to the input transform technique, we can use the indirect technique route to obtain the convergence of the output sequence. Finally, it is shown that in the case the input-output coupling matrix is full-column rank, we can directly analyze the convergence of the output sequence with resort to output transform technique.