A simpler stability criterion for a class of nonlinear systems

A simpler stability criterion is presented here that is useful for predicting limit cycles in a class of second-order non-linear control systems. The criterion is developed simply from a study of the roots of the system characteristic equation. It is shown that the limit cycle predicted by this criterion is stable if the slope of the
a/b^{2}
-locus at the intersection point is positive, while a negative slope indicates an unstable limit cycle.