Discrete-Time Models for Implicit Port-Hamiltonian Systems
This work provides a method for preserving port-Hamiltonian structure in discrete-time models, which is important for numerical simulation and control design of such systems.
The paper studies implicit representations of finite-dimensional port-Hamiltonian systems and shows how to construct a sampled-data model that preserves the port-Hamiltonian structure under sample and hold.
Implicit representations of finite-dimensional port-Hamiltonian systems are studied from the perspective of their use in numerical simulation and control design. Implicit representations arise when a system is modeled in Cartesian coordinates and when the system constraints are applied in the form of additional algebraic equations (the system model is in a DAE form). Such representations lend themselves better to sample-data approximations. An implicit representation of a port-Hamiltonian system is given and it is shown how to construct a sampled-data model that preserves the port-Hamiltonian structure under sample and hold.