Singular controls for port-Hamiltonian systems (Theory of singularities of smooth mappings and around it)

The port-Hamiltonian system is a generalized Hamiltonian system and is regarded as an especial input-output control system. We see the port-Hamiltonian systems from the viewpoint of geometric control theory. Controllability and observability are basic concepts in control theory and important for system design. Singular controls play an important role in a control system, especially in the sense of optimal control problem. We see the following properties are equivalent for linear port-Hamiltonian systems: controllability, observability and nonexistence of singular control.