Transmission Zero Assignment in Linear Multivariable Systems; Part II: The General Case

In this paper, we present a computational procedure for modifying a given (not necessarily square) proper rational function matrix such that it has a desired set of transmission zeros. The modification consists of the addition of a proper rational function matrix which under certain conditions will have the same set of poles as the given matrix. The computational procedure uses reductions (performed with orthogonal transformations) employed in a numerically stable technique for computing transmission zeros, and a recent numerically reliable approach for eigenvalue assignment using output feed-back. The results of this paper together with a reliable eigenvalue assignment algorithm provide the numerical tools for modifying a given system such that it has a desired set of poles and transmission zeros.