Noncausal Zames-Falb Multipliers for Tighter Estimates of Exponential Convergence Rates

Zames-Falb multipliers are useful for proving the stability of nonlinear feedback loops, using either classical passivity theory or the theory of integral quadratic constraints. Recent papers have introduced new classes of such multipliers for proving exponential stability with guaranteed convergence rates. We extend these recent results to allow for noncausal multipliers and thereby reduce the conservativeness of the estimates of the exponential convergence rates.