LMI search for rational anticausal Zames-Falb multipliers

Given a linear time-invariant plant, the search of a suitable multiplier over the class of Zames-Falb multiplier is a challenging problem which has been studied for several decades. Recently, a new linear matrix inequality search has been proposed over rational and causal Zames-Falb multipliers. This paper analyzes the conservatism of the restriction to causality on the multipliers and presents a complementary search for rational and anticausal multipliers.