abstract
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.
key words: reciprocity; passive system; linear system; controllability; observability; behaviors; electrical networks.