A condition of the eigenvalues of detection filters for disturbance attenuation: an invariant zero approach

This paper investigates the response characteristics of detection filters and proposes a condition of disturbance attenuation by analyzing the distribution of the closed-loop eigenvectors with respect to the eigenvalues. As an invariant factor of the detection space, invariant zeros are selected. It is shown that the closed-loop eigenvectors are determined by the linear equations of eigenvalues utilizing the one-to-one correspondence between the eigenvectors and the invariant zero vectors. Based on this result, we present a condition of the eigenvalues associated with the disturbances to reduce their effect in the output space for the case of disturbance accommodation.