We consider feedback interconnections composed of a linear system whose input-output behavior is constrained by a relation. It is shown how to analyze stability of such interconnections by suitably refining the general framework of integral quadratic constraints. For the special case of static multivalued monotone nonlinearities, we reveal that one can employ Zames-Falb multipliers in order to substantially reduce conservatism if compared with passivity-based approaches and as illustrated with a numerical example. Our results are expected to open up an avenue towards a systematic stability analysis of data-integrated systems.
%0 Conference Paper
%1 SchHol18
%A Scherer, Carsten W.
%A Holicki, Tobias
%D 2018
%J IFAC-PapersOnLine
%K myown from:tobiasholicki EXC310 pn4 peerReviewed imng
%N 25
%P 390-395
%R 10.1016/j.ifacol.2018.11.138
%T An IQC theorem for relations: Towards stability analysis of data-integrated systems
%U https://doi.org/10.1016/j.ifacol.2018.11.138
%V 51
%X We consider feedback interconnections composed of a linear system whose input-output behavior is constrained by a relation. It is shown how to analyze stability of such interconnections by suitably refining the general framework of integral quadratic constraints. For the special case of static multivalued monotone nonlinearities, we reveal that one can employ Zames-Falb multipliers in order to substantially reduce conservatism if compared with passivity-based approaches and as illustrated with a numerical example. Our results are expected to open up an avenue towards a systematic stability analysis of data-integrated systems.
@inproceedings{SchHol18,
abstract = {We consider feedback interconnections composed of a linear system whose input-output behavior is constrained by a relation. It is shown how to analyze stability of such interconnections by suitably refining the general framework of integral quadratic constraints. For the special case of static multivalued monotone nonlinearities, we reveal that one can employ Zames-Falb multipliers in order to substantially reduce conservatism if compared with passivity-based approaches and as illustrated with a numerical example. Our results are expected to open up an avenue towards a systematic stability analysis of data-integrated systems.},
added-at = {2021-10-18T15:37:00.000+0200},
author = {Scherer, Carsten W. and Holicki, Tobias},
biburl = {https://puma.ub.uni-stuttgart.de/bibtex/212e3a488448a875bc66a9b126291bb26/mathematik},
doi = {10.1016/j.ifacol.2018.11.138},
interhash = {a72906b9181da73efbb0f5e877c5baee},
intrahash = {12e3a488448a875bc66a9b126291bb26},
journal = {IFAC-PapersOnLine},
keywords = {myown from:tobiasholicki EXC310 pn4 peerReviewed imng},
number = 25,
pages = {390-395},
timestamp = {2023-10-31T14:48:40.000+0100},
title = {An IQC theorem for relations: Towards stability analysis of data-integrated systems},
url = {https://doi.org/10.1016/j.ifacol.2018.11.138},
volume = 51,
year = 2018
}
