  Zames-Falb multipliers are mathematical constructs which can be used to prove
stability of so-called Lur'e systems: systems that consist of a feedback
interconnection of a linear element and a static nonlinear element. The main
advantage of Zames-Falb multipliers is that they enable "passivity"-like
results to be obtained but with a level of conservatism much lower than
\emph{pure} passivity results. However, some of the papers describing the
development of the Zames-Falb multiplier machinery are somewhat abstruse and
not entirely clear. This article attempts to provide a relatively simple
construction of Zames and Falb's main results which will hopefully be
understandable to most graduate-level control engineers.
