On the response of nonlinear control systems to periodic input signals

In this paper we study a broad class of nonlinear control systems containing a single memoryless nonlinear element. We present conditions under which there exists a unique periodic response, with a given period, to an arbitrary periodic input with the same period, and we derive an upper bound on the mean-square error incurred by applying the describing-function technique. The expression for the error reflects the intuitive engineering arguments that are often employed to justify the use of the describing-function method. Conditions are also presented under which subharmonic response components and self-sustained oscillations cannot occur.