A note on causal and CITE iterative learning control algorithms

Time and frequency domain convergence properties of causal and Current Iteration Tracking Error (CITE) discrete time Iterative Learning Control (ILC) algorithms are discussed. Considering necessary and sufficient convergence conditions basic matrix properties can be utilized to show that causal as well as CITE ILC algorithms converge to zero error in only very restrictive special cases. The frequency domain convergence conditions, sufficient for monotone convergence, are studied using a discrete-time version of Bode’s integral theorem. The result is that causal and CITE ILC algorithms will not satisfy the frequency domain conditions except if the system has relative degree zero or it is accepted that the algorithms do not converge to zero error.