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arXiv · 2106.15913

Zames-Falb Multipliers: don't panic

Matthew C. Turner
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Abstract

Zames-Falb multipliers are mathematical constructs which can be used to prove stability of so-called Lur'e systems: systems that consist of a feedback interconnection of a linear element and a static nonlinear element. The main advantage of Zames-Falb multipliers is that they enable "passivity"-like results to be obtained but with a level of conservatism much lower than \emph{pure} passivity results. However, some of the papers describing the development of the Zames-Falb multiplier machinery are somewhat abstruse and not entirely clear. This article attempts to provide a relatively simple construction of Zames and Falb's main results which will hopefully be understandable to most graduate-level control engineers.

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Matthew C. Turner. 2021-06-30. Zames-Falb Multipliers: don't panic. https://arxiv.org/abs/2106.15913

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