Disturbance decoupling by state feedback and pd control law for systems with direct feedthrough matrices

In this paper new geometric necessary and sufficient conditions are provided for the solvability of the exact disturbance decoupling problem with a control input consisting of a static state feedback and a PD function of the signal to be rejected, with the requirement of internal stability of the closed loop. Differently from previous results presented in the literature on this issue, we not restrict our attention to strictly proper systems. Indeed, both feedthrough matrices from the control and from the disturbance to the output was considered to be possibly non-zero.