Computation of Zames-Falb multipliers revisited

The convex approach to the absolute stability problem is considered. Gapski and Geromel´s algorithm for computing Zames-Falb multipliers, used in determining stability, treats the problem as an optimization problem. It is found that their algorithm may terminate prematurely in some cases, failing to find the optimal multiplier. We propose an improvement that always finds an ascent direction and a multiplier that improves the objective function whenever one exists.