(A, B)-invariant and stabilizability subspaces, a frequency domain description

In a paper of E. Emre and the author a polynomial characterization for (A, B)-invariant subspaces is given. The characterization is used to give a frequency domain criterion for the solvability of the disturbance decoupling problem. In this paper a more elementary and simpler treatment is given. Furthermore, stabilizability subspaces are introduced, are given a frequency domain characterization and are used to solve design problems.