Comments on “Decentralized iterative learning control for a class of large scale interconnected dynamical systems” by Hansheng Wu [J. Math. Anal. Appl. 327 (2007) 233–245]

In the reference paper Wu (2007) [1], a decentralized iterative learning control (ILC) algorithm is proposed aiming at achieving the asymptotic convergence of output errors for a class of linear time-varying large scale interconnected dynamic systems. The key points in the analysis of this decentralized ILC are the adoption of a specific time-weighted norm, and the use of a property of nondecreasing real functions that leads to the cancellation of interactions between subsystems. Here, on the one hand, we show that there exists a derivation problem in the proof, thus the asymptotic convergence property cannot be obtained. On the other hand, we provide an alternative analysis method, the classical contraction-mapping based ILC analysis with the lambda-norm, to demonstrate that the decentralized ILC algorithm is still valid and able to achieve the asymptotic convergence.