LMI-based design of robust iterative learning control schemes with finite frequency range tracking specifications

Many systems compete the same finite duration task over and over again, where once each is complete the system resets to the starting location and the next one begins. Each execution is known as a trial and the duration the trial length. Iterative learning control has been developed for such systems where the distinguishing feature is the use of information from previous trials to update the control signal applied on the next one. The new contributions in this paper are for algorithms that use a feedforward filter often termed the learning filter. A condition for existence of this filter is formulated in terms of linear matrix inequalities through application of the generalized Kalman-Yakubovich-Popov lemma. This allows filter design over a finite, as opposed to the complete, frequency range which is more practically relevant in many cases. An extension to systems with uncertainties represented by a polytopic description is also developed using parameter dependent Lyapunov functions.