GRAPH-THEORETIC CHARACTERIZATION OF FIXED MODES IN FREQUENCY-DOMAIN

We examine a characterization of fixed modes in a frequency-domain fra mework based on the graphical representation of systems with multiple poles. We present a graph-theoretic characterization of the characteri stic polynomials of closed-loop systems under arbitrary structural con straints. Based on this characterization, fixed modes are characterize d using the weight products of 1-factors of the weighted directed grap hs associated with closed-loop systems. It is also shown that the well -known characterization of fixed modes in terms of transmission zeros can be derived from the proposed graph-theoretic characterization. Cop yright (C) 1996 Elsevier Science Ltd.