Title data
Björnsson, Jóhann ; Giesl, Peter ; Hafstein, Sigurdur Freyr ; Kellett, Christopher M. ; Li, Huijuan:
Computation of continuous and piecewise affine Lyapunov functions by numerical approximations of the Massera construction.
Department of Mathematics, University of Bayreuth
Bayreuth
,
2014
. - 6 S.
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Project information
Project title: |
Project's official title Project's id Marie-Curie Initial Training Network "Sensitivity Analysis for Deterministic Controller Design" (SADCO) 264735-SADCO The Icelandic Research Fund, Grant 130677- 052 ARC Future Fellowship FT1101000746 Humboldt Research Fellowship No information |
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Project financing: |
7. Forschungsrahmenprogramm für Forschung, technologische Entwicklung und Demonstration der Europäischen Union Icelandic Centre for Research; Australian Research Council; Alexander von Humboldt Foundation |
Abstract
The numerical construction of Lyapunov functions provides useful information on system behavior. In the Continuous and Piecewise Affine (CPA) method, linear programming is used to parameterize a CPA Lyapunov function for continuous nonlinear systems. This method is relatively slow due to the linear program that has to be solved. A recent proposal was to parameterize the CPA Lyapunov function based on a Lyapunov function in a converse Lyapunov theorem by Yoshizawa. In this paper we propose parameterizing CPA Lyapunov functions using a Lyapunov function construction in a classic converse Lyapunov theorem by Massera. We provide the theory for such a parameterization and present several examples to illustrate the utility of this approach.
Further data
Item Type: | Preprint, postprint |
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Additional notes (visible to public): | erschienen in:
Proceedings of the IEEE 53rd Annual Conference on Decision and Control Held in Los Angeles, California, 2014. - Los Angeles, CA, USA : Institute of Electrical and Electronics Engineers (IEEE) , 2014 . - S. 5506-5511 ISBN 978-1-4799-7746-8 DOI: https://doi.org/10.1109/CDC.2014.7040250 |
Keywords: | Lyapunov methods; nonlinear control systems; asymptotic stability; linear programming; Massera construction; approximation methods; continuous systems |
DDC Subjects: | 500 Science > 510 Mathematics |
Institutions of the University: | Faculties Faculties > Faculty of Mathematics, Physics und Computer Science Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics) Profile Fields Profile Fields > Advanced Fields Profile Fields > Advanced Fields > Nonlinear Dynamics |
Language: | English |
Originates at UBT: | Yes |
URN: | urn:nbn:de:bvb:703-epub-1956-1 |
Date Deposited: | 25 Mar 2015 11:28 |
Last Modified: | 01 Jun 2021 09:33 |
URI: | https://epub.uni-bayreuth.de/id/eprint/1956 |