We show that quadratic constraints admit a semi-algebraic interpretation of dynamic systems. This allows us to improve the analysis of polynomial systems under nonlinear feedback laws by use of the general S-procedure. Extending results to integral quadratic constraints, with the aid of LaSalle’s invariance theorem, we obtain a general stability proof for a larger class of multipliers. Numerical results show that the resulting hierarchy of sum-of-squares problems yields much better stability estimates for an exemplary unstable system with nonlinear stabilizing feedback than local approximations.
%0 Journal Article
%1 cunis2024semialgebraic
%A Cunis, Torbjørn
%A Pfifer, Harald
%D 2024
%J Automatica
%K myown
%N 111549
%R 10.1016/j.automatica.2024.111549
%T A semi-algebraic view on quadratic constraints for polynomial systems
%U https://www.sciencedirect.com/science/article/pii/S0005109824000414
%V 163
%X We show that quadratic constraints admit a semi-algebraic interpretation of dynamic systems. This allows us to improve the analysis of polynomial systems under nonlinear feedback laws by use of the general S-procedure. Extending results to integral quadratic constraints, with the aid of LaSalle’s invariance theorem, we obtain a general stability proof for a larger class of multipliers. Numerical results show that the resulting hierarchy of sum-of-squares problems yields much better stability estimates for an exemplary unstable system with nonlinear stabilizing feedback than local approximations.
@article{cunis2024semialgebraic,
abstract = {We show that quadratic constraints admit a semi-algebraic interpretation of dynamic systems. This allows us to improve the analysis of polynomial systems under nonlinear feedback laws by use of the general S-procedure. Extending results to integral quadratic constraints, with the aid of LaSalle’s invariance theorem, we obtain a general stability proof for a larger class of multipliers. Numerical results show that the resulting hierarchy of sum-of-squares problems yields much better stability estimates for an exemplary unstable system with nonlinear stabilizing feedback than local approximations.},
added-at = {2024-02-10T19:28:27.000+0100},
author = {Cunis, Torbjørn and Pfifer, Harald},
biburl = {https://puma.ub.uni-stuttgart.de/bibtex/20a6393ab62b3a4ee1bcf062d4455b7b6/ifr},
doi = {10.1016/j.automatica.2024.111549},
interhash = {d51b03cf462c126c127b1a8cd249ba82},
intrahash = {0a6393ab62b3a4ee1bcf062d4455b7b6},
issn = {0005-1098},
journal = {Automatica},
keywords = {myown},
number = 111549,
timestamp = {2024-12-11T14:59:19.000+0100},
title = {A semi-algebraic view on quadratic constraints for polynomial systems},
url = {https://www.sciencedirect.com/science/article/pii/S0005109824000414},
volume = 163,
year = 2024
}
