Abstract: This peper is mainly devoted to the study of three kinds of characterizations of simultaneous invariant subspaces, i.e., time domain characterization, frequency domain characterization, and geometric characterization. In particular, the paper gives a new description of the largest simultaneous invariant subspace contained in a given subspace H. Based on these results, a necessary and suffcient condition for robust disturbance decoupling problem of discrete perturbation systems is first given. Then, by extending the discuss to the continuous perturbation case. a Kharitonov-like result is derived. Thus, robust disturbance decoupling problems under two kinds of perturbations are entirely solved in theory.