A stability inequality for nonlinear feedback systems with slope-restricted nonlinearity

Using Lyapunov's direct method, a stability inequality in frequency domain is derived for nonlinear feedback systems with slope-restricted nonlinearity. In the present approach, a transformed system that involves the slope of the nonlinearity is considered, thus leading to a stability inequality that incorporates the slope information (but not the sector information) of the nonlinearity. The approach is essentially an extension of a recent idea of the author.