Stability of a Class of Non-linear Time-varying Systems

Abstract

It is shown that a criterion for the asymptotic stability-in-the-Iarge of systems containing a single time-varying non-linearity can be stated in the form of a frequency-domain inequality involving the product of a multiplier and the transfer function of the linear part. Several sub-classes of monotone increasing non-linearities are considered and it is observed that when the non-linearity has a restricted odd asymmetry and a suitably restricted rate of time-variation, the multiplier can have complex conjugate poles and zeros. The results obtained indicate that as more conditions are imposed on the non-linear function, either (1) a higher rate of time-variation can be allowed in a given sector containing the non-linearity, or (2) for a given tolerable rate of time-variation, the permissible sector for the non-linearity can be widened.