A new concept, undisturbability, is formally defined and related to the concepts of uncontrollability and structural controllability. Necessary and sufficient conditions for a system to have undisturbable state or output variables are expressed in terms of the structure of the coefficient matrices in the state-space model and the structure of the eigenvector matrix. These results and an eigenvector/eigenvalue assignment algorithm (Srinathkumar and Rhoten 1975, Shahet al. 1975) provide the basis of a design procedure for synthesizing multivariable controllers which achieve disturbance localization.