A Stability Analysis Based on Dissipativity of Linear and Nonlinear Repetitive Control

This paper deals with repetitive control (RC). More specifically, a parametrised version of the repetitive compensator, i.e. of the infinite-dimensional controller employed in RC schemes, modelled as a boundary control system (BCS) in port-Hamiltonian form is presented. Well-posedness and stability of such control scheme are rigorously addressed thanks to novel tools based on dissipativity theory and originally developed for the stabilisation of BCS. Here, the linear and the nonlinear cases are tackled, and in both the cases the classes of plants for which RC schemes are exponentially stable are determined. Moreover, and explicit motivation of perfect asymptotic tracking and disturbance rejection for exponentially stable RC systems without relying on the internal model theory is provided. To show the validity of the analysis, simulations are reported. (C) 2019, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.