Condensed Forms for linear Port-Hamiltonian Descriptor Systems

Motivated by the structure which arises in the port-Hamiltonian formulation of constraint dynamical systems, we derive structure preserving condensed forms for skew-adjoint differential-algebraic equations (DAEs). Moreover, structure preserving condensed forms under constant rank assumptions for linear port-Hamiltonian differential-algebraic equations are developed. These condensed forms allow us to further analyze the properties of port-Hamiltonian DAEs and to study e.g. existence and uniqueness of solutions. As examples the equations of motion of linear multibody systems and of linear electrical circuit equations are considered