Repetitive control of positive real systems via delayed feedback is Lyapunov asymptotically stable

In this paper, we are concerned with the analysis of linear infinite-dimensional control systems that should be able to compensate and/or track signals that are periodic. Adopting the name given in the seminal paper by Hara et al., we call them repetitive controllers. We analyze the asymptotic stability in the Lyapunov sense of finite-dimensional positive real plants coupled with pure delays. For this class of systems, we initially prove convergence in the weak topology to later deduce convergence in the strong one. Index Terms--Control systems, delay systems, linear systems, Lyapunov methods.