The generalized pole assignment problem

For some Linear, strictly proper system given by its transfer function, two dynamic output feedback problems can be posed. The first one is that of using dynamic-output feedback to assign the closed-loop characteristic polynomial and the second that of assigning the closed-loop invariant factors. We are concerned with these problems and their inter-relationships. The formulation is done in the frequency domain and the investigation carried out from an algebraic point of view, in terms of linear equations over rings of polynomials. Using the notion of genericity, we express several necessary and sufficient conditions.