Computation of continuous and piecewise affine Lyapunov functions by numerical approximations of the Massera construction

URN to cite this document: urn:nbn:de:bvb:703-epub-1956-1

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
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
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

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