Determination of perturbation index of a DAE with maximum weighted matching algorithm

There are several definitions of the index of a differential algebraic equation (DAE). Based on these definitions, algorithms are derived to calculate and reduce the index. Pantelides (1988) has used the differential index to construct his well known algorithm. We propose to use the perturbation index. This naturally leads to finding the highest power of s of each element in (As+B)^-1. These highest powers determine the perturbation index of DAE Ax´+Bx=f(t). With fast graph-oriented algorithms this highest power can be found and, consequently, the perturbation index can be determined