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 m th-degree numerator polynomial and n th-degree denominator polynomial ( m \leq n ). 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 m . In this short paper, a technique is described whereby the case m = n can be transformed to the case m . By this means, some of the results that heretofore were restricted to the case m can be successfully applied to the case m = n . 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 m = n .