On reciprocal systems and controllability

TL;DR

This paper extends classical results on signature symmetric and passive realizations to uncontrollable systems, providing algebraic conditions for behaviors realizable by electrical networks with resistors, inductors, capacitors, and transformers.

Contribution

It introduces necessary and sufficient algebraic conditions for realizing behaviors as electrical networks, including uncontrollable systems, expanding the scope of classical realization theory.

Findings

Characterization of uncontrollable signature symmetric realizations

Algebraic conditions for electrical network realizability

Extension of classical results to non-controllable systems

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.