In this note it is shown that the famous multiplier absolute stability test of R. O'Shea, G. Zames and P. Falb is necessary and sufficient if the set of Lur'e interconnections is lifted to a Kronecker structure and an explicit method to construct the destabilizing static nonlinearity is presented.
%0 Journal Article
%1 KhaSch22
%A Kharitenko, Andrey
%A Scherer, Carsten W.
%D 2022
%K from:carsten.scherer pn4 prePrint EXC2075 imng
%T On the exactness of a stability test for Lur'e systems with slope-restricted nonlinearities
%X In this note it is shown that the famous multiplier absolute stability test of R. O'Shea, G. Zames and P. Falb is necessary and sufficient if the set of Lur'e interconnections is lifted to a Kronecker structure and an explicit method to construct the destabilizing static nonlinearity is presented.
@article{KhaSch22,
abstract = {In this note it is shown that the famous multiplier absolute stability test of R. O'Shea, G. Zames and P. Falb is necessary and sufficient if the set of Lur'e interconnections is lifted to a Kronecker structure and an explicit method to construct the destabilizing static nonlinearity is presented.},
added-at = {2023-02-24T09:02:32.000+0100},
archiveprefix = {arXiv},
author = {Kharitenko, Andrey and Scherer, Carsten W.},
biburl = {https://puma.ub.uni-stuttgart.de/bibtex/2f612691f039e9422bf8b049130ba076b/mathematik},
eprint = {2210.14992},
file = {:http\://arxiv.org/pdf/2210.14992v1:PDF},
interhash = {2311ca64370b7bd2f9f2dcdbc28776f8},
intrahash = {f612691f039e9422bf8b049130ba076b},
keywords = {from:carsten.scherer pn4 prePrint EXC2075 imng},
month = oct,
primaryclass = {math.OC},
timestamp = {2023-11-01T18:41:25.000+0100},
title = {On the exactness of a stability test for Lur'e systems with slope-restricted nonlinearities},
year = 2022
}