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

Abstract

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.