Smoothing control of discrete linear repetitive processes

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, a repetitive process makes a series of sweeps or passes through dynamics defined on a finite duration. At the end of each pass, the process returns to the starting point and the next pass begins. The novel feature is that the output on the previous pass acts as a forcing function on, and hence contributes to, the current pass output. There has been a considerable volume of profitable work on the development of a control theory for such processes but currently the most effective control law design algorithms are based on sufficient but not necessary stability conditions and hence conservativeness may prevent the design of control laws in some cases. This paper considers the design of a new control law which exploits extra available information to allow stabilizing control law design.