Geometric methods in the theory of singular 2-D linear systems

A geometric approach for systems represented by a singular 2D Fornasini-Marchesini model is developed by introducing suitable notions of invariant subspace and controlled invariant subspace of the state space. The first notion is shown to be usefull in characterizing the set of compatible boundary conditions and in studying the existence and uniqueness of solutions to the state space equation of the considered models. The second notion is proved to be relevant in investigating the solvability of a Disturbance Decoupling Problem and is employed for stating a constructive sufficient condition for the existence of solutions to such problem.