On the structure at infinity of a structured system

AbstractWe develop a graph-theoretic characterization of the generic structure at infinity of the transfer matrix of a structured system. We show that the generic structure at infinity can be determined by means of algorithms from combinatorial optimization based on the max-flow min-cut theorem, and on results concerning minimal-cost flows. As an application of the obtained characterization, we propose a structural version of two well-known disturbance decoupling problems, and we derive graph-theoretic necessary and sufficient conditions for the solvability of each of the two problems