Nonnormality estimation in projection-type system realization methods

Using Henrici’s departure from normality as tool, we investigate the influence of nonnormality on the spectral sensitivity of system matrices of projection-type system realization methods. Basically, we show that the system matrix of one of these methods is diagonally similar to the system matrix of the classical Kung’s method and then conclude that the spectral sensitivity of all methods decreases significantly under condition that are often met or easy to impose in practice. Based on these results, we conclude that all projection-type realization methods have essentially the same spectral properties as Kung’s method. Furthermore, a theoretical eigenvalue error bound is derived and illustrated by numerical simulations.