The Controllability Question

The solvability question for systems of partial differential equations: the Fundamental Principal of Malgrange and Palamadov [1,2]. The question dual to the solvability question.
Controllability for state space systems; its generalisation to distributed systems given as kernels of differential operators defined over the ring $A=\mathbb{C}[\delta_1,\dots,\delta_n]$ of constant coefficient pde; the functor $\mathsf{Hom}_A(-,\mathcal{F})$, where $\mathcal{F}$ is a space of distributions on $\mathbb{R}^n$; the description of the $A$-module structure of $\mathcal{D}'$ , the space of distributions on $\mathbb{R}^n$, and of $\mathcal{C}^{\infty}, \mathcal{S}'$ etc.