Zames–Falb Multipliers for Invariance

This letter provides a comprehensive framework for local stability analysis of uncertain feedback interconnections within the integral quadratic constraints theory using general dynamic multipliers. It is shown how so-called hard and soft constraints can be effectively combined in order to (locally) capture the action of the uncertainty. This is illustrated for Zames-Falb multipliers, where it is proven that the subclasses of causal and anticausal multipliers can easily be factorized into hard constraints and thus individually be incorporated into the framework without introducing conservatism.