On invariant zeros of linear systems of PDEs

In this paper we provide a behavioral framework in which to describe and extend the concept of linear dynamics introduced by Fliess, from the one dimensional (1D) to the multidimensional (nD) framework. We provide an alternative description of the invariant zeros of a system, equivalent to the Smith zero description in the 1D case and use this to generalize the concept and characterization of invariant zeros to the nD case. In particular we show that the definitions are equivalent in the 1D case to those in the classical literature. We provide new results on the structural relations of nD invariant and transmission zeros.