A graph-theoretic characterization for the rank of nonlinear systems

Based on the definition of the differential output rank, a generic rank similar to the one of Nijmeijer (1986) is introduced. Moreover, in analogy to the conditions in linear systems theory, a directed graph G describing the structure of nonlinear systems is presented. The development of a relation between G and the generic rank is the main result of this paper. In addition the subclasses of nonlinear systems for which the generic rank coincides with the differential output rank are characterized. By this relation it is possible to find two different graph-based algorithms suitable for the computer-aided calculation of rho *. Finally computational results comparing the acceleration achieved by standard and graph-based concepts are given.