Bond graph determination of system matrix determinant of descriptor systems

In this paper, a graph-theoretic characterization of the system matrix determinant coefficients is given. The result applies to the class of structured LTI descriptor systems intrinsically associated with any linear causal bond graph. Starting from the expansion of a matrix determinant by means of the permutation group, permutation cycles are sorted and the expression is factorized. It is shown that each factor has a bond graph interpretation by means of multicycles and input/output-multipaths. In this way, each factor is determined by the properties (gain and order) of a path-cycle family. The result is illustrated through a case study in vehicle dynamics.