Computing Invariant Zeros of a MIMO Linear System Using State-Space Realization

Poles of a multi-input multi-output (MIMO) linear system can be computed by solving an eigenvalue problem; however, the problem of computing its invariant zeros is equivalent to a generalized eigenvalue problem. This paper revisits the problem of computing the invariant zeros by solving an eigenvalue problem. We introduce a realization called the invariant zero form in which the system's invariant zeros are isolated in a partition of the transformed dynamics matrix. It is shown that the invariant zeros are then the eigenvalues of a partition of the transformed dynamics matrix. Although the paper's main result is proved only for square MIMO systems, the technique can be heuristically extended to nonsquare MIMO systems, as shown in the numerical examples.