On the response of time-variable nonlinear systems to almost periodic signals

Abstract It is of interest in automatic control and in circuit theory to be able to tell whether a nonlinear system has the following property, basic to many engineering discussions: that if ω 1 , ω 2 ,… are the frequencies present in the input, then the output contains at most the frequencies of the form ∑ i=1 n ϰ i ω i with k i integers. In the present work sufficient conditions for this property to occur are given for two important classes of nonlinear systems containing a single non-linearity. These conditions are, roughly, that the nonlinearity be sufficiently smooth and that a certain function arising from the linear part of the system have an integral less than unity.