On the internal signature and minimal electric network realizations of reciprocal behaviors
Provides theoretical bounds for reciprocal system realizations, relevant to control theory and network synthesis, but is an incremental extension of known results.
The paper establishes new lower bounds on the number of even-parity (capacitor) and odd-parity (inductor) states in reciprocal systems that may be uncontrollable, extending prior results on signature-symmetric realizations and electric network synthesis.
In a recent paper, it was shown that (i) any reciprocal system with a proper transfer function possesses a signature-symmetric realization in which each state has either even or odd parity; and (ii) any reciprocal and passive behavior can be realized as the driving-point behavior of an electric network comprising resistors, inductors, capacitors and transformers. These results extended classical results to include uncontrollable systems. In this paper, we establish new lower bounds on the number of states with even parity (capacitors) and odd parity (inductors) for reciprocal systems that need not be controllable.