Geometric criterion for the absence of limit cycles in nonlinear control systems

In most autonomous systems, the generation of periodic modes is considered to be an instability. Considering feedback systems composed of a time-invariant linear operator in cascade with an odd memoryless nonlinearity, a method is derived which provides a geometric interpretation of frequency regions in the Nyquist plane, over which simple oscillations cannot occur. This criterion answers a question of system behaviour when the Popov criterion is violated.