An energy-based, continuous-valued measure of interaction between the input and output channels of a linear constant system is formulated and used as the basis for a theory of near disturbance localization for discrete-time systems. The generalized disturbance localization problem is formulated as the minimization problem of finding the feedback gain matrixFfor which this interaction measure is minimized. The solutions obtained are shown to correspond where appropriate with those predicted by the geometric state-space approach. Connections are made, too, to results on system invertibility and on ‘cheap’ linear-quadratic control problems.