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arXiv · 1812.02397

Convex searches for discrete-time Zames-Falb multipliers

Joaquin Carrasco·William P. Heath·Nur Syazreen Ahmad·Shuai Wang·Jingfan Zhang
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Abstract

In this paper we develop and analyse convex searches for Zames--Falb multipliers. We present two different approaches: Infinite Impulse Response (IIR) and Finite Impulse Response (FIR) multipliers. The set of FIR multipliers is complete in that any IIR multipliers can be phase-substituted by an arbitrarily large order FIR multiplier. We show that searches in discrete-time for FIR multipliers are effective even for large orders. As expected, the numerical results provide the best $\ell_{2}$-stability results in the literature for slope-restricted nonlinearities. Finally, we demonstrate that the discrete-time search can provide an effective method to find suitable continuous-time multipliers.

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Joaquin Carrasco, William P. Heath, Nur Syazreen Ahmad, Shuai Wang, Jingfan Zhang. 2018-12-06. Convex searches for discrete-time Zames-Falb multipliers. https://doi.org/10.1109/tac.2019.2958848

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