  We study computational methods for computing the distance to singularity, the
distance to the nearest high index problem, and the distance to instability for
linear differential-algebraic systems (DAEs) with dissipative Hamiltonian
structure. While for general unstructured DAEs the characterization of these
distances is very difficult, and partially open, it has been recently shown
that for dissipative Hamiltonian systems and related matrix pencils there exist
explicit characterizations. We will use these characterizations for the
development of computational methods to compute these distances via methods
that follow the flow of a differential equation converging to the smallest
perturbation that destroys the property of regularity, index one or stability.
