Frequency domain stability criteria--Part I

The objective of this paper is to illustrate the limitations of the generalized Popov Theorem in establishing the stability of a loop containing a single nonlinearity, and to use the Liapunov Theory to give a new frequency domain stability criterion for such systems. The new criterion differs from Popov's in that less restrictive assumptions are made on the linear part, and stronger assumptions are made on the nonlinearity. In this paper, it is assumed that the nonlinearity is monotone increasing. The approach used here is quite general, however, and in a companion paper various other restrictions are considered.