An improved stability criterion for a system with a non-monotone non-linearity

Abstract

An improved frequency-do main criterion has been derived for the asymptotic stability in the large (ASIL) of an autonomous system containing a single non-linearity. The non-linearity is assumed to belong to a new class of non-monotone functions having properties intermediate to monotone increasing functions and the functions considered in the Popov criterion. The stability criterion derived requires that Z(s) G(s) be positive real, where Z(s) is a restricted R-L driving point impedance and G(a) is the transfer function of the linear part of the system. It is further shown that stability can be established in certain cases even when the polar plot of the linear part transfer function lies in all the four quadrants and the non-linearity is neither monotone nor odd.