Some issues in the geometric theory of infinite dimensional systems

In this paper, adapting some ideas recently developed in the context of systems over rings, we investigate the properties of the subset of the invariant subspaces for a particular class of infinite dimensional systems, and we analyze especially the connections between such subspaces, the notion of zero and the static, state-feedback disturbance decoupling problem. Motivations for this study are provided by the existence of analogies between the geometry of infinite dimensional systems and that of systems over ring in some interesting cases (e.g. for delay-differential systems). The main result obtained is a new necessary and sufficient condition for the existence of solutions to the disturbance decoupling problem for the considered class of systems