Stability of feedback systems containing a single odd monotonic nonlinearity

In this paper the stability of a feedback system with a single odd monotonic nonlinearity is considered. It is shown that if a multiplier
Z(s)
having a specific form exists so that
G(s) Z^{\pm1}(s)
is positive real, the feedback system is asymptotically stable for every odd monotonic function lying in the first and third quadrants. The multiplier
Z(s)
suggested can have both complex poles and complex zesro. A simple example is included to demonstrate the applicability of the criterion developed.