In this note, we give a systematic new analysis of disturbance decoupling problems for standard linear time-invariant systems based on the theory of matrix pencils. This approach is based on the computation of condensed forms under orthogonal equivalence transformations. From these forms, that can be computed in a numerically stable way, we obtain new necessary and sufficient conditions that are numerically verifiable, and, furthermore, we immediately obtain numerically stable algorithms to compute the desired compensators, We present a numerical example that demonstrates the properties of the new approach.