  A wide class of matrix pencils connected with dissipative Hamiltonian
descriptor systems is investigated. In particular, the following properties are
shown: all eigenvalues are in the closed left half plane, the nonzero finite
eigenvalues on the imaginary axis are semisimple, the index is at most two, and
there are restrictions for the possible left and right minimal indices. For the
case that the eigenvalue zero is not semisimple, a structure-preserving method
is presented that perturbs the given system into a Lyapunov stable system.
