Multipliers for Nonlinearities With Monotone Bounds

We consider Lurye (sometimes written Lur’e) systems, whose nonlinear operator is characterized by a possibly multivalued nonlinearity that bounded above and below monotone functions. Stability can be established using subclass of the Zames–Falb multipliers. The result generalizes similar approaches in literature. Appropriate multipliers found convex searches. Because used for nonlinearities, they applied after loop transformation. illustrate power new with two examples: one continuous time other discrete time: first, approach shown to outperform available stability tests literature; second, we focus on special case asymmetric saturation important consequences systems nonzero steady-state exogenous signals.