  Recently, negative imaginary and counter-clockwise systems have attracted
attention as an interesting class of systems, which is well-motivated by
applications. In this paper first the formulation and extension of negative
imaginary and counter-clockwise systems as (nonlinear) input-output Hamiltonian
systems with dissipation is summarized. Next it is shown how by considering the
time-derivative of the outputs a port-Hamiltonian system is obtained, and how
this leads to the consideration of alternate passive outputs for
port-Hamiltonian systems. Furthermore, a converse result to positive feedback
interconnection of input-output Hamiltonian systems with dissipation is
obtained, stating that the positive feedback interconnection of two linear
systems is an input-output Hamiltonian system with dissipation if and only if
the systems themselves are input-output Hamiltonian systems with dissipation.
This implies that the Poisson and resistive structure matrices can be redefined
in such a way that the interaction between the two systems only takes place via
the coupling term in the Hamiltonian of the interconnected system.
Subsequently, it is shown how network interconnection of (possibly nonlinear)
input-output Hamiltonian systems with dissipation results in another
input-output Hamiltonian system with dissipation, and how this leads to a
stability analysis of the interconnected system in terms of the Hamiltonians
and output mappings of the systems associated to the vertices, as well as the
topology of the network.
