Dynamic disturbance decoupling of nonlinear systems and linearization

In this paper we investigate the connections between the solvability of the dynamic disturbance decoupling problem with exponential stability (DDDPes) for a nonlinear system and the solvability of the same problem for its linearization around an equilibrium point. It is shown that under generic conditions the nonlinear DDDPes is solvable for a nonlinear system if and only if the static disturbance decoupling problem with stability (DDPs) is solvable for its linearization around an equilibrium point