Disturbance decoupling for linear time-invariant systems: a matrix pencil approach

We give a new systematic 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, which 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.