TY - JOUR

T1 - Phase Limitations of Multipliers at Harmonics

AU - Heath, William P.

AU - Carrasco, Joaquin

AU - Zhang, Jingfan

PY - 2024/1/1

Y1 - 2024/1/1

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

U2 - 10.1109/tac.2023.3271855

DO - 10.1109/tac.2023.3271855

M3 - Erthygl

VL - 69

SP - 566

EP - 573

JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

SN - 2334-3303

IS - 1

ER -