Bond graph-based determination of characteristic polynomial of descriptor systems

In this paper, it is given a graph-oriented procedure to determine the characteristic polynomial of a descriptor system. The proof relies on the expansion of a matrix’ determinant by means of the permutation group. It is shown that (after factorization) permutation cycles are mapped one-to-one with families in the bond graph. This relationship only holds because of the structured nature of the equations. Gain and order of those families are then used to derive polynomial coefficients. The result applies to the class of structured LTI descriptor systems intrinsically associated with any linear causal bond graph.