A graph-theoretic characterization for the rank of the transfer matrix of a structured system

Abstract

In this paper structured systems are considered and the generic rank of the transfer matrix of such systems is introduced. It is shown that this rank equals the maximum number of vertex disjoint paths from the input vertices to the output vertices in the graph that can be associated to the structured system. This maximum number of disjoint paths can be calculated using techniques from combinatorics. As an application a structural version of the well-known almost disturbance decoupling problem is proposed.