On the necessity and sufficiency of the Zames–Falb multipliers for bounded operators

This paper analyzes the robust feedback stability of a single-input-single-output stable linear time-invariant (LTI) system against three different classes nonlinear systems using Zames–Falb multipliers. The contribution is threefold. Firstly, we identify class uncertain over which equivalent to existence an appropriate multiplier. Secondly, when restricted be static (a.k.a. memoryless), such coincides with sloped-restricted monotone nonlinearities , and classical result multipliers ensure recovered. Thirdly, LTI, first demonstrated subset second, multiplier shown sufficient but not necessary for stability.