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

The now well-known techniques introduced by Lyapunov have led to many very interesting results concerning the stability of time-varying nonlinear feedback systems governed by systems of differential equations. However, these methods have by 110 means led to a definitive theory of stability for even the simplest nontrivial time-varying nonlinear feedback systems. The general problem is, of course, one of considerable difficulty. The unparalleled utility of the Nyquist stability criterion for singleloop, linear, time-invariant feedback systems is directly attributable to the fact that it is an explicit frequency-domain condition. The Nyquist locus not only indicates the stability or instability of a system, it presents the information in such a way as to aid the designer in arriving at a suitable design. The criterion is useful even in cases in which the system is so complicated that a sufficiently accurate analysis is not feasible, since experimental measurements can be used to construct the loop-gain locus. The primary purpose of this article is to point out that some recently 1601