Computation of Zero Directions of Transfer Functions

In this note we describe a state space approach to compute so-called zero directions of a rational transfer function H(). The method works on the coeecient matrices of a minimal state space realization of the transfer function H() and does not require its Taylor expansion around each zero. Moreover, it uses only unitary transformations to nd the structure at each zero. 1. Background and deenitions Finding zeros and their structural indices is a problem that occurs naturally when one wants to describe the solution set of particular matrix equations involving rational matrices 4, 5, 7] and has recently received attention in the context of interpolation problems 1]. The structure at a point 0 which is a pole or a zero of a transfer function H() is deened via the Smith McMillan form of the m n rational matrix H() at the point 0 : M() H() N() = 2 6 6 6 6 4