Absolutely stable systems with a differentiable nondecreasing nonlinearity

Sufficient conditions are found to absolute stability in the positive sector of the Hurwitz angle $(0, K)$ for systems with one differentiable nondecreasing nonlinearity that do not require construction of changed frequency responses. These conditions are shown to be met if the Nyquist curves of the linear part are convex, in particular, in single-loop systems with any number of stable static first- and second-order elements with the oscillation index of the oscillating elements less than unity. Relations of zeros and poles of the transfer function are given that are bound to insure absolute stability in the angle.