An off-axis circle criterion for stability of feedback systems with a monotonic nonlinearity

An off-axis circle criterion is stated in this paper as a sufficient condition for the stability of a nonlinear feedback system with a single monotonic nonlinearity. The criterion provides a geometric method for determining a sector
(K_{1} < [F(y_{1})-F(y_{2})]/ (y_{1}-y_{2}) < K_{2})
with in which the nonlinearity may lie for asymptotic stability. The relation between the criterion stated and the well-known Popov criterion and the circle criterion for time-varying systems is also discussed. Two examples are included to clarify various aspects of the criterion and its relation to existing results.