A Geometric Analysis of the Zeros and Residues via the Dual GHR

The Dual Generalized Hessenberg Representation (Dual GHR) is a canonic form for single input single output systems which identifies the input output properties of the system. Here it is shown how the Dual GHR can be used to identify almost pole-zero canceliations and small residues of the corresponding poles. This connection between the state space representation and transfer function is established using geometrical arguments. Near unobservability and near uncontrollability, measures relying on angles between subspaces, play a key role.