An algorithm for the calculation of transmission zeros of the system (C, A, B, D) using high gain output feedback

A new algorithm, which is an extension of [1, algorithm II], is presented to determine the transmission zeros of the system
\dot{x}=Ax+Bu, y=Cx+Du
denoted by
(C,A,B,D)
. The algorithm is based on the observation that for nondegenerate
(C,A,B,D)
systems, the set of transmission zeros of
(C,A,B,D)
are contained in the finite eigenvalues of the closed-loop system matrix
{A + BK((I_{r}/p)-DK)^{-1}C}
where
K
is any arbitrary matrix of full rank,
y \in R^{r}
, and
\rho\rightarrow\infty
. Some numerical examples of systems of 100th order are included to illustrate the algorithm.