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

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.
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 . - pp. 5506-5511
ISBN 978-1-4799-7746-8
DOI: https://doi.org/10.1109/CDC.2014.7040250

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Official URL: Volltext

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Project information

Project title:
Project's official titleProject's id
Marie-Curie Initial Training Network "Sensitivity Analysis for Deterministic Controller Design" (SADCO)264735-SADCO
The Icelandic Research Fund, Grant130677- 052
ARC Future FellowshipFT1101000746
Humboldt Research FellowshipNo information

Abstract in another language

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 compute 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 compute the CPA Lyapunov function based on a Lyapunov function in a converse Lyapunov theorem by Yoshizawa. In this paper we propose computing CPA Lyapunov functions using a Lyapunov function construction in a classic converse Lyapunov theorem by Massera. We provide the theory for such a computation and present several examples to illustrate the utility of this approach.

Further data

Item Type: Article in a book
Refereed: Yes
Keywords: Lyapunov methods; nonlinear continuous systems; asymptotic stability; linear programming; Massera construction; approximation methods
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
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 01 Apr 2015 06:19
Last Modified: 01 Apr 2015 06:19
URI: https://eref.uni-bayreuth.de/id/eprint/9539

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