Considerations on the zero-dynamics of port Hamiltonian systems and application to passive implement

In this work a passive control scheme for port Hamiltonian systems with dissipation (PHD) that is able to conserve the PHD structure of the dynamics of the system when constrained over a sub-manifold of the state space is presented. The idea is to modify the interconnection and damping structure of the system and to add a proper dynamical extension in such a way that the constraint could be related with some dynamical invariant of the resulting closed-loop system. Since part of the structure of this dynamical extension can be arbitrarily chosen, it is also possible to drive the state of the system on the constraint and to clearly obtain the dynamical behavior that the constraint de?nes. If a proper variable structure dynamical extension is chosen, it is possible to achieve a sliding-mode like behavior that can be suitable to some energetic considerations.