LMI searches for anticausal and noncausal rational Zames–Falb multipliers

• Published in: Systems & control letters Vol. 70; pp. 17 - 22
• Main Authors: Carrasco, Joaquin, Maya-Gonzalez, Martin, Lanzon, Alexander, Heath, William P.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01-08-2014
• Subjects: Multiplier search; Slope-restricted nonlinearities; Zames–Falb multipliers; Zames–Falb multipliers; Multiplier search; Slope-restricted nonlinearities
• ISSN: 0167-6911; 1872-7956
• DOI: 10.1016/j.sysconle.2014.05.005

Given a linear time-invariant plant, the search for a suitable multiplier over the class of Zames–Falb multipliers 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 letter analyzes the conservatism of the restriction to causality on the multipliers and presents a complementary search for rational and anticausal multipliers. The addition of a Popov multiplier to the anticausal Zames–Falb multiplier is implemented by analogy with the causal search. As a result, a search over a noncausal subset of Zames–Falb multipliers is obtained. A comparison between all the search methods proposed in the literature is given.