Problems and Results in a Geometric Approach to the Theory of Systems over Rings

The use of geometric methods in the study of linear systems with coefficients in a ring presents several difficulties, but, as in the case of coefficients in a field, it appears capable of providing efficient solutions to a number of control and observation problems. In this paper we survey some recent results concerning a class of Disturbance Decoupling Problems and we extend the techniques developed in that case to a class of problems concerning the Estimation of Linear Functions of the State.