A note on control systems with one nonlinear element

An important class of nonlinear control systems can be represented by a single-loop negative feedback circuit having one isolated, instantaneous type, nonlinear element in series with a linear transfer function with th-degree numerator polynomial and th-degree denominator polynomial ( ). In the literature on automatic control, many of the techniques and theorems associated with this class of systems are restricted in application to the special case . In this short paper, a technique is described whereby the case can be transformed to the case . By this means, some of the results that heretofore were restricted to the case can be successfully applied to the case . In particular, this procedure, together with a certain theorem about nonlinear functions with feedback, makes it possible to apply some recent results in absolute stability to certain cases of .