In this letter, we revisit structure exploiting SDP solvers dedicated to the solution of Kalman-Yakubovic-Popov semi-definite programs (KYP-SDPs). These SDPs inherit their name from the KYP lemma and they play a crucial role in, e.g., robustness analysis, robust state feedback synthesis, and robust estimator synthesis for uncertain dynamical systems. Off-the-shelve SDP solvers require O(n^6) arithmetic operations per Newton step to solve this class of problems, where n is the state dimension of the dynamical system under consideration. Specialized solvers reduce this complexity to O(n^3) . However, existing specialized solvers do not include semi-definite constraints on the Lyapunov matrix, which is necessary for controller synthesis. In this letter, we show how to include such constraints in structure exploiting KYP-SDP solvers.
%0 Journal Article
%1 gramlich2023structure
%A Gramlich, D.
%A Holicki, T.
%A Scherer, C. W.
%A Ebenbauer, C.
%D 2023
%J IEEE Control Syst. Lett.
%K PN4-3(II) PN4 EXC2075 selected
%P 1831-1836
%R 10.1109/LCSYS.2023.3277314
%T A Structure Exploiting SDP Solver for
Robust Controller Synthesis
%V 7
%X In this letter, we revisit structure exploiting SDP solvers dedicated to the solution of Kalman-Yakubovic-Popov semi-definite programs (KYP-SDPs). These SDPs inherit their name from the KYP lemma and they play a crucial role in, e.g., robustness analysis, robust state feedback synthesis, and robust estimator synthesis for uncertain dynamical systems. Off-the-shelve SDP solvers require O(n^6) arithmetic operations per Newton step to solve this class of problems, where n is the state dimension of the dynamical system under consideration. Specialized solvers reduce this complexity to O(n^3) . However, existing specialized solvers do not include semi-definite constraints on the Lyapunov matrix, which is necessary for controller synthesis. In this letter, we show how to include such constraints in structure exploiting KYP-SDP solvers.
@article{gramlich2023structure,
abstract = {In this letter, we revisit structure exploiting SDP solvers dedicated to the solution of Kalman-Yakubovic-Popov semi-definite programs (KYP-SDPs). These SDPs inherit their name from the KYP lemma and they play a crucial role in, e.g., robustness analysis, robust state feedback synthesis, and robust estimator synthesis for uncertain dynamical systems. Off-the-shelve SDP solvers require O(n^6) arithmetic operations per Newton step to solve this class of problems, where n is the state dimension of the dynamical system under consideration. Specialized solvers reduce this complexity to O(n^3) . However, existing specialized solvers do not include semi-definite constraints on the Lyapunov matrix, which is necessary for controller synthesis. In this letter, we show how to include such constraints in structure exploiting KYP-SDP solvers.},
added-at = {2024-03-26T11:56:14.000+0100},
author = {Gramlich, D. and Holicki, T. and Scherer, C. W. and Ebenbauer, C.},
biburl = {https://puma.ub.uni-stuttgart.de/bibtex/2aca72e39e622da877b3c50f894739894/exc2075},
doi = {10.1109/LCSYS.2023.3277314},
interhash = {19b517913fcb20a4757e31a46ce6f4a4},
intrahash = {aca72e39e622da877b3c50f894739894},
journal = {IEEE Control Syst. Lett. },
keywords = {PN4-3(II) PN4 EXC2075 selected},
pages = {1831-1836},
timestamp = {2024-03-26T11:56:14.000+0100},
title = {A Structure Exploiting SDP Solver for
Robust Controller Synthesis},
volume = 7,
year = 2023
}
