The absolute sensitivity matrix

Transfer function matrices describing dynamical systems depend in a complex way upon large numbers of physical parameters, which often are not known precisely. A fundamental problem in sensitivity theory is to write such matrices as the sum of a nominal matrix and an error matrix, the latter expressing the effects of parameter variations. This error matrix is the absolute sensitivity matrix. In earlier work, the authors have given a general expression for the absolute sensitivity matrix associated with a wide class of network and systems problems. An approximation to the absolute sensitivity matrix was also brought forth and shown to be related to the well known Cruz-Perkins sensitivity matrix. The relation of the absolute sensitivity matrix to the Cruz-Perkins matrix was weakened, in the early work, by the approximation which had been made in derivation. The present paper establishes the exact conditions under which the absolute sensitivity matrix is directly related to the Cruz-Perkins matrix.