On the control discrete linear repetitive processes with smoothing effects*

Repetitive processes are a distinct class of two-dimensional (2D) systems (i.e. information propagation in two independent directions occurs) of both systems theoretic and applications interest. In particular, these processes are characterized by a series of sweeps through dynamics defined over a finite duration where the output produced on the previous pass critically contributes to the current one and so on. Also the process is reset before the start of each new pass and in the majority of the currently known results it is assumed that the previous pass profile is unaffected by the resetting and other not directly modeled effects. In practice this may not be the case and in such cases there is a need to adequately represent this feature in the models used for analysis. In this paper control law design algorithms for one representation of the case when the previous pass profile is significantly modified before the next pass begins are developed.