Absolute stability criteria for multiple slope-restricted monotonic nonlinearities

Absolute stability criteria such as the classical Popov criterion guarantee stability for a class of sector-bounded nonlinearities. Although the sector restriction bounds the admissible class of the nonlinearities, the local slope of the nonlinearity may be arbitrarily large. In this paper the authors derive absolute stability criteria for multiple slope-restricted time-invariant monotonic nonlinearities. Like the Popov criterion, in the single-input/single-output case the authors' results provide a simple graphical interpretation involving a straight line in a modified Popov plane.>