Uniqueness of Circuits and Systems Containing One Nonlinearity

S. Boyd and L. O. Chua

IEEE Transactions on Automatic Control, TAC-30(7):674-681, July 1985.
Also in Mathematical Theory of Networks and Systems, Lecture Notes in Control and Information Sciences, 58:101-119, June 1983.

We study systems containing one memoryless nonlinearity. We show that two such systems have the same I/O operator only when they are related by simple scaling, delay, and loop transformations. The theory is applied to one-port networks containing one nonlinear element.