Phase Limitations of Multipliers at Harmonics

William P. Heath; Joaquin Carrasco; Jingfan Zhang

doi:10.1109/tac.2023.3271855

Phase Limitations of Multipliers at Harmonics

William P. Heath, Joaquin Carrasco, Jingfan Zhang

Research output: Contribution to journal › Article › peer-review

Abstract

The absolute stability of a Lurye system with a monotone nonlinearity is guaranteed by the existence of a suitable O'Shea–Zames–Falb (OZF) multiplier. We develop a numerically tractable phase condition under which there can be no suitable OZF multiplier for the transfer function of a given continuous-time plant. We provide its graphical interpretation. The condition may be tested in a systematic manner and leads to significantly improved results compared with the condition in the literature from which it is derived. Our results are useful to evaluate the performance of numerical searches for OZF multipliers

Original language	Unknown
Pages (from-to)	566–573
Journal	IEEE Transactions on Automatic Control
Volume	69
Issue number	1
Early online date	1 May 2023
DOIs	https://doi.org/10.1109/tac.2023.3271855
Publication status	Published - 1 Jan 2024
Externally published	Yes

Access to Document

10.1109/tac.2023.3271855

http://dx.doi.org/10.1109/TAC.2023.3271855

Cite this

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title = "Phase Limitations of Multipliers at Harmonics",

abstract = "The absolute stability of a Lurye system with a monotone nonlinearity is guaranteed by the existence of a suitable O'Shea–Zames–Falb (OZF) multiplier. We develop a numerically tractable phase condition under which there can be no suitable OZF multiplier for the transfer function of a given continuous-time plant. We provide its graphical interpretation. The condition may be tested in a systematic manner and leads to significantly improved results compared with the condition in the literature from which it is derived. Our results are useful to evaluate the performance of numerical searches for OZF multipliers",

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AU - Carrasco, Joaquin

AU - Zhang, Jingfan

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N2 - The absolute stability of a Lurye system with a monotone nonlinearity is guaranteed by the existence of a suitable O'Shea–Zames–Falb (OZF) multiplier. We develop a numerically tractable phase condition under which there can be no suitable OZF multiplier for the transfer function of a given continuous-time plant. We provide its graphical interpretation. The condition may be tested in a systematic manner and leads to significantly improved results compared with the condition in the literature from which it is derived. Our results are useful to evaluate the performance of numerical searches for OZF multipliers

AB - The absolute stability of a Lurye system with a monotone nonlinearity is guaranteed by the existence of a suitable O'Shea–Zames–Falb (OZF) multiplier. We develop a numerically tractable phase condition under which there can be no suitable OZF multiplier for the transfer function of a given continuous-time plant. We provide its graphical interpretation. The condition may be tested in a systematic manner and leads to significantly improved results compared with the condition in the literature from which it is derived. Our results are useful to evaluate the performance of numerical searches for OZF multipliers

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