Phase Limitations of Multipliers at Harmonics

William Heath; Joaquin  Carrasco; Jingfan Zhang

doi:10.1109/TAC.2023.3271855

Phase Limitations of Multipliers at Harmonics

William Heath, Joaquin Carrasco, Jingfan Zhang

EEE - Academic & Research

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	English
Pages (from-to)	1-8
Number of pages	8
Journal	IEEE Transactions on Automatic Control
DOIs	https://doi.org/10.1109/TAC.2023.3271855
Publication status	E-pub ahead of print - 1 May 2023

Keywords

Delays
Machine-to-machine communications
Numerical stability
Power system stability
Stability criteria
Systematics
Transfer functions

Access to Document

10.1109/TAC.2023.3271855

Cite this

@article{3c7aa44703ff41e3bd4a649567dd96e6,

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.",

keywords = "Delays, Machine-to-machine communications, Numerical stability, Power system stability, Stability criteria, Systematics, Transfer functions",

author = "William Heath and Joaquin Carrasco and Jingfan Zhang",

year = "2023",

month = may,

day = "1",

doi = "10.1109/TAC.2023.3271855",

language = "English",

pages = "1--8",

journal = "IEEE Transactions on Automatic Control",

issn = "0018-9286",

publisher = "IEEE",

}

TY - JOUR

T1 - Phase Limitations of Multipliers at Harmonics

AU - Heath, William

AU - Carrasco, Joaquin

AU - Zhang, Jingfan

PY - 2023/5/1

Y1 - 2023/5/1

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.

KW - Delays

KW - Machine-to-machine communications

KW - Numerical stability

KW - Power system stability

KW - Stability criteria

KW - Systematics

KW - Transfer functions

U2 - 10.1109/TAC.2023.3271855

DO - 10.1109/TAC.2023.3271855

M3 - Article

SN - 0018-9286

SP - 1

EP - 8

JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

ER -

Phase Limitations of Multipliers at Harmonics

Abstract

Keywords

Access to Document

Fingerprint

Cite this