On simplifying a graphical stability criterion for linear distributed feedback systems

In an earlier publication [1], Vidyasagar proposed to derive a standard Nyquist-type stability criterion [1, theorem 1] from a result about a graphical test developed by Callier and Desoer [2, theorem 2]. The attempt suffers from two major weaknesses which are detailed in the Appendix. Basically, Vidyasagar's concept is correct: namely, it is possible to give a graphical test which relies exclusively on the graph of
\acuteangle (1 + k\hat{g}(j\omega))
, the phase of the return difference. We give below a correct statement and proof of such a graphical test.