Further results on 1D state space models for discrete linear repetitive processes

The general question considered in this paper is how to embed the 2D dynamics of discrete linear repetitive processes into a standard (1D) linear state space model for control related analysis. Previous work had obtained a partial answer in the form of an affine model structure due to a time varying term arising from the initial conditions on each pass. This paper shows how this term can be removed by state variable transformations and hence complete the solution of this general question