A frequency domain condition for boundedness of learning control using a forgetting factor

If there exist errors of initial setting, measurement noises, or system fluctuations, it is common to introduce a forgetting factor into iterative learning control for the case of not using the derivative of the tracking error. This paper deals with the learning control with the forgetting factor for general linear systems and presents a rigorous frequency domain condition under which the tracking error is bounded. An explicit bound of the tracking error is also provided, which suggests a suitable selection of the forgetting factor.