Eigenvalue sensitivity of some transfer function realizations

In this correspondence the eigenvalue sensitivities of the following transfer function realizations are calculated: controllable canonical form, observable canonical form, Jordan canonical form, and a particular realization for complex eigenvalues. From these results it is shown that the controllable and observable canonical forms may be less sensitive than the Jordan canonical form and the realization for complex eigenvalues. The general formulas are applied to second-order systems with complex eigenvalues.