Stability analysis of asymmetric saturation via generalised Zames-Falb multipliers

We consider Lurye (sometimes written Lur´e) systems whose nonlinearity may be time-varying but is bounded above and below by time-invariant monotone nonlinearities. Stability can be established using a sub-class of the Zames-Falb multipliers. The result generalises similar approaches in the literature. Interesting results can be found for nonlinearities that are monotone and bounded by odd nonlinearities. We focus on the special case for asymmetric saturation and include loop transformations in the analysis. There are important consequences for systems with non-zero steady state exogenous signals. We illustrate with an example that demonstrates what is, in effect, a local stability result.