Structured system models Part 2. Directed graphs and boolean matrices

Parameterized system models and their augmented controllability indices are studied. Analytically parameterized system models arc shown to have generic index lists, i.e. lists which arc actual lists for all parameter values except those in a proper analytic variety. For structured system models, as a subset of analytically parameterized system models, there exists a known graph-theoretic method for determining the Hermite indices. A new method for examining both Hermite and Kronecker indices is introduced. The method is based on a necessary graph-theoretic condition for the examined columns of the controllability matrix to be linearly independent. Additional sufficient conditions are given to complete the method. The given graph-theoretic results are also expressed using boolean matrices associated with graphs.