On Factorization, Interconnection and Reduction of Collocated Port-Hamiltonian Systems

Based on a geometric interpretation of nonlinear balanced reduction some implications of this approach are analyzed in the case of collocated port-Hamiltonian systems which have a certain balance in its structure. Furthermore, additional examples of reduction for this class of systems are presented.

Lumped Approximation of a Transmission Line with an Alternative Geometric Discretization

An electromagnetic one-dimensional transmission line represented in a distributed port-Hamiltonian form is lumped into a chain of subsystems which preserve the port-Hamiltonian structure with inputs and outputs in collocated form. The procedure is essentially an adaptation of the procedure for discretization of Stokes-Dirac structures presented previously, that does not preserve the port-Hamiltonian structure after discretization. With some modifications essentially inspired on the finite difference paradigm, the procedure now results in a system that preserves the collocated port-Hamiltonian structure along with some other desirable conditions for interconnection. The simulation results are compared with those presented previously.

Energy-Storage Balanced Reduction of Port-Hamiltonian Systems

Supported by the framework of dissipativity theory, a procedure based on physical energy to balance and reduce port-Hamiltonian systems with collocated inputs and outputs is presented. Additionally, some relations with the methods of nonlinear balanced reduction are exposed. Finally a structure-preserving reduction method based on singular perturbations is shown.