Structure preserving model reduction of port-Hamiltonian systems

It is shown that by use of the Kalman-decomposition an uncontrollable and/or unobservable port-Hamiltonian system is reduced to a controllable/observable system that inherits a port-Hamiltonian structure. Energy and co-energy variable representations for port-Hamiltonian systems are discussed and the reduction procedures are used for both representations. These exact reduction procedures motivate two approximate reduction procedures structure preserving for a general port-Hamiltonian system in scattering representation, Effort- and Flow-constraint reduction methods.