Structure indices for multidimensional systems

The structure indices of a one-dimensional system are an important set of invariants. In this paper we examine a generalization of this concept to multidimensional linear systems, which corresponds to the algebraic concept of a Hilbert series. We use the standard theory of the Hilbert series to explain some of the previous 1D system-theoretic results. We discuss the computation of nD structure indices from an initial condition set, and the invariants which can be derived from these indices