Discrete multidimensional systems over ZnZn

We generalize the theory of multidimensional, discrete, linear, shift-invariant systems from the well-investigated case in which the signals take their values in a field, to the situation where these values belong to a finite ring of the form Z/nZZ/nZ. Some basic systems theoretic properties are studied and characterized: autonomy, input–output decompositions, controllability, and observability.