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Implicit representations of finite-dimensional port-Hamiltonian systems arestudied from the perspective of their use in numerical simulation and controldesign. Implicit representations arise when a system is modeled in Cartesiancoordinates and when the system constraints are applied in the form ofadditional algebraic equations (the system model is in a DAE form). Suchrepresentations lend themselves better to sample-data approximations. Animplicit representation of a port-Hamiltonian system is given and it is shownhow to construct a sampled-data model that preserves the port-Hamiltonianstructure under sample and hold.

Discrete-Time Models for Implicit Port-Hamiltonian Systems