H_∞ filtering for a class of 2D systems

The unique characteristic of a repetitive process is a series of sweeps or passes through a set of dynamics defined over a finite duration known as the pass length. At the end of each pass, the process is reset and the next time through the output, or pass profile, produced on the previous pass acts as a forcing function on, an hence contributes to, the dynamics of the new pass profile. They are hence a class of systems with information propagation in two independent directions where here the dynamics over the finite pass length are described by a matrix linear differential equation and that from pass to pass has a discrete updating structure. This means that filtering/estimation theory/algorithms for, in particular, 2D discrete linear systems is not applicable. In this paper we solve a general filtering problem with a view toward use in the many applications where such action will be required.