  In this paper, we treat extended balancing for continuous-time linear
time-invariant systems, and we address the problem of structure-preserving
model reduction of the subclass of port-Hamiltonian systems. We establish
sufficient conditions to ensure that the reduced-order model preserves a
port-Hamiltonian structure. Moreover, we show that the use of extended Gramians
can be exploited to get a small error bound and, possibly, to preserve a
physical interpretation for the reduced-order model.
