  In this paper, we extend classical results on (i) signature symmetric
realizations, and (ii) signature symmetric and passive realizations, to systems
which need not be controllable. These results are motivated in part by the
existence of important electrical networks, such as the famous Bott-Duffin
networks, which possess signature symmetric and passive realizations that are
uncontrollable. In this regard, we provide necessary and sufficient algebraic
conditions for a behavior to be realized as the driving-point behavior of an
electrical network comprising resistors, inductors, capacitors and
transformers.
