Fixed poles of almost disturbance decoupling by state feedback

When the almost disturbance decoupling problem (ADDP) is solvable, some poles of the closed loop system are fixed for any state feedback solution. In Zou and Malabre (2009c), the authors have characterized them by means of some invariant zeros but in the particular case of (A, B)-controllable systems. As a complement, here, we give the characterization of the fixed poles of ADDP for the general case, namely without any controllability assumption. We also propose a method to solve the ADDP for this general case, as well as a numerical example to illustrate our contributions.