An off-axis circle criterion for feedback control systems with a sector nonlinearity

Describes a graphical evaluation of the robust stability in a frequency domain based on the results from our previous papers in which Popov´s criterion was expressed in an explicit form. The control system described herein is a feedback system with one time-invariant nonlinear element (a sector nonlinearity) in the forward path. By applying the small gain theorem that concerns L₂ gain in regard to a nonlinear subsystem with a free parameter, a robust stability condition for control systems with time-invariant nonlinearity is presented. Using this concept, we show a representation of an off-axis circle criterion on a Nyquist diagram, and propose an evaluation method of the stability from the relative position with the vector locus of the open loop frequency response characteristic