Exact disturbance decoupling by a proportional-derivative state feedback law

This paper investigates the role of a proportional-derivative(P.D.) state feedback control law, u = F1x + F2x, for a time-invariant linear system in the context of almost controlled invariant subspaces. The disturbance decoupling problem is considered and it is shown that the solvability criterion for the almost disturbance decoupling problem given by Willems corresponds to the existence of a control law which uses state derivative feedback and which achieves exact disturbance decoupling.