Dynamic process initial conditions in repetitive processes. Controllability and stability analysis

Repetitive, or multipass, processes are a class of 2D systems of both practical and algorithmic/theoretical interest whose dynamics cannot be analysed or controlled using standard (1D) systems theory. Recently it has been shown that the modelling of the boundary conditions, also known as the process initial conditions, is a crucial feature in the analysis and control of these processes. This paper presents some further results on the effects of so-called `dynamic´ process initial conditions on the controllability and stability properties of discrete linear repetitive processes. Previous work has shown that these dynamic process initial conditions alone can destroy the stability properties of these processes. Hence their effects must be `adequately´ accounted for the process modelling stage in order to ensure that subsequent analysis does not lead to incorrect results/conclusions. The main results developed in this paper can be summarised as follows. (i) Computationally efficient stability tests which can, in effect, be applied using standard, or 1D, linear systems tests. (ii) Characterisation of so-called pass controllability in the form of matrix rank based conditions. (iii) Conditions under which the dynamic process initial conditions can be selected to ensure stability and pass controllability