Zames-Falb multipliers for absolute stability: From O´Shea´s contribution to convex searches

Absolute stability attracted much attention in the sixties. Several stability conditions for loops with slope-restricted nonlinearities were developed. Results such as the Circle Criterion and the Popov Criterion form part of the core curriculum for students of control. Moreover, the equivalence of results obtained by different techniques, specifically Lyapunov and Popov´s stability theories, led to one of the most important results in control engineering: the KYP Lemma.