Joaquin Carrasco

TL;DR: 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.

TL;DR: Correct application of the conditions still gives an improvement over absolute stability criteria in the literature for at least one example, but some of the claims for lack of conservativeness in the above technical note should be moderated.

TL;DR: The conservatism of the restriction to causality on the multipliers is analyzed and the addition of a Popov multiplier to the anticausal Zames–Falb multiplier is implemented by analogy with the causal search.

TL;DR: Two less conservative LMI conditions for discrete-time systems with slope-restricted nonlinearities are constructed, derived via Lyapunov theory and the theory of integral quadratic constraints and noncausal Zames-Falb multipliers.

TL;DR: The subclass is shown to be phase-equivalent to the class of discrete-time rational noncausal Zames-Falb multipliers, and can be expressed as an LMI (linear matrix inequality) whose number of parameters increases quadratically with model order andwhose number of linear constraints increases linearly with model orders.