Proportional plus integral control and disturbance rejection for differential linear repetitive processes

Repetitive processes are a distinct class of two-dimensional systems (i.e. information propagates in two independent directions) of both systems theoretic and applications interest. They cannot be controlled by direct extension of existing techniques from either standard (termed 1D in the associated literature) or two-dimensional (2D) systems theory. Most of the currently available results for them focus on fundamental properties such as stability, controllability etc. Recently, however, there has been a move (prompted by the progress in this earlier research) towards the development of a control theory, and associated design algorithms, for the subclasses of so-called differential and discrete linear repetitive processes which arise in applications such as iterative learning control. In this paper we continue this theme by investigating the role of proportional plus integral action in the differential case.