Frequency-domain instability criteria for time-varying and nonlinear systems

Recent research has produced a number of frequency-domain stability criteria applicable to linear systems having nonlinear and/or time-varying feedback. One of the more interesting of these stability criteria is the so-called Circle Criterion which represents a generalization of the familiar result of Nyquist. The present paper provides a basis for generating instability counterparts of most of the available frequency-domain stability criteria. The procedure is described in detail for the Circle Criterion. Once the general pattern is established it becomes a simple matter to generate instability counterparts of other similar stability criteria. Several worked examples are included to illustrate the theory. The paper has been written with both the general reader and the specialist in mind; it is hoped that both will find something of interest.