On reciprocal systems and controllability
For control theorists and electrical engineers, it addresses a gap in realization theory for uncontrollable systems, motivated by examples like Bott-Duffin networks.
The paper extends classical results on signature symmetric and passive realizations to uncontrollable systems, providing necessary and sufficient algebraic conditions for a behavior to be realized as the driving-point behavior of an electrical network with RLC elements and transformers.
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.