Disturbance decoupling and robustness of stability

In this paper we investigate the interaction of disturbance decoupling requirement with the robustness of closed loop stability in the sense of normalized coprime factor perturbations. The disturbance decoupling and the robust stabilization requirements are expressed in terms of the subspace valued functions associated to plant and controller and an upper bound on robustness of stability imposed by the disturbance decoupling requirement is derived. This is then compared with the actual robustness of stability that can be achieved by a solution of the disturbance decoupling problem for systems having left invertible transfer matrix from the control inputs to the controlled outputs.