A Frequency-Domain Condition for the Stability of Feedback Systems Containing a Single Time-Varying Nonlinear Element

Abstract

It is proved that a condition similar to the Nyquist criterion guarantees the stability (in an important sense) of a large class of feedback systems containing a single time-varying nonlinear element. In the case of principal interest, the condition is satisfied if the locus of a certain complex-valued function (a) is bounded away from a particular disk located in the complex plane, and (b) does not encircle the disk.