Algebraic characterization of approximate controllability of behaviours of spatially invariant systems

An algebraic characterization of the property of approximate controllability is given, for behaviours of spatially invariant dynamical systems, consisting of distributional solutions w, that are periodic in the spatial variables, to a system of partial differential equations [formula presented] corresponding to a polynomial matrix M ∈ (C[ξ1,...,ξd,τ])m×n. This settles an issue left open in Sasane (2004).