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 < n
. In this short paper, a technique is described whereby the case
m = n
can be transformed to the case
m < n
. By this means, some of the results that heretofore were restricted to the case
m < n
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
.