Repetitive processes are a distinct class of 2D systems (i.e. information propagation 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 here) or 2D systems theory. Here, we give new results on the relatively open problem of the design of physically based control laws using an LMI setting. These results are for the sub-class of the so-called discrete linear repetitive processes which arise in applications areas such as iterative learning control. (C) 2004 Elsevier Ltd. All rights reserved.