When Finite-Region Stability meets iterative learning control

Some recent papers have extended the concept of finite-time stability (FTS) to the context of 2-D linear systems, where it has been referred to as finite-region stability (FRS). To this regard, the novel contribution of our work considers an interesting application of FRS to the context of iterative learning control (ILC). In particular, a new procedure is proposed so that the tracking error of the ILC law converges within the desired bound in a finite number of iterations. The results provided in the paper lead to an optimization problem constrained by linear matrix inequalities (LMIs), that can be solved via widely available software. A numerical example illustrates the effectiveness of the proposed technique.