ID representations and systems theory for a class of 2D linear systems

Repetitive, or multipass, processes are a class of systems characterised by a series of sweeps through a set of dynamics defined over a finite fixed duration. The class of so-called discrete linear repetitive processes have strong-structural links with well studied classes of 2D linear systems and also with standard (1D) linear systems. One possible approach to the (control related) analysis of these processes is to embed their basic 2D structure in a 1D representation. This paper develops such a representation and uses it to characterise the key systems theoretic property of controllability for this class of linear repetitive processes.