Port-Hamiltonian system, Descriptor system, Differential-algebraic equation, Strangeness index, System transformation, Skew-adjoint pair of matrix functions, Condensed form.
Motivated by the structure which arises in the port-Hamiltonian formulation of constraint dynamical systems, structure preserving condensed forms for skew-adjoint differential-algebraic equations (DAEs) are derived. Moreover, structure preserving condensed forms under constant rank assumptions for linear port-Hamiltonian differential-algebraic equations are developed. These condensed forms allow for the further analysis of the properties of port-Hamiltonian DAEs and to study, e.g., existence and uniqueness of solutions or to determine the index. It can be shown that under certain conditions for regular port-Hamiltonian DAEs the strangeness index is bounded by $\mu\leq1$.
"Condensed Forms for Linear Port-Hamiltonian Descriptor Systems",
Electronic Journal of Linear Algebra,
Volume 35, pp. 65-89.