A Generalized Zames-Falb Multiplier

Lur´e systems represent feedback interconnections of a Linear Time-Invariant system with a nonlinear operator. The Zames-Falb criterion is a powerful tool to determine the stability of a Lur´e system when the nonlinear operator is defined by a monotonic, odd and single-valued function. The article provides a generalization of the Zames-Falb criterion for the analysis of stability of a Lur´e system for nonlinear static operators that are “approximately” monotonic and odd. This result extends the standard Zames-Falb criterion with an additional notion of “robustness”.