A Unified Analysis Tool in Iterative Learning Control: Composite Energy Function

Usually, the convergence analysis of a continuous-time iterative learning control (ILC) algorithm is carried out by using either Contraction Mapping (CM) or Composite Energy Function (CEF) based methods. They are subtly different in terms of types of systems to which it can be applied, the convergence properties, convergence condition and the standing assumptions. Although the link between these two methods has been observed in literature, there is no clear statement to show that CEF-based method can be served as a unified analysis tool. This paper shows this fact by re-proving the well-known CM-based convergence results of P-type ILC algorithms using a novel CEF method.