Title data
Hafstein, Sigurdur Freyr ; Kellett, Christopher M. ; Li, Huijuan:
Continuous and piecewise affine Lyapunov functions using the Yoshizawa construction.
Department of Mathematics, University of Bayreuth
Bayreuth
,
2013
. - 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 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 Australian Research Council; Alexander von Humboldt Foundation |
Abstract
We present a novel numerical technique for the computation of a Lyapunov function for nonlinear systems with an asymptotically stable equilibrium point. Our proposed approach constructs a continuous piecewise affine (CPA) function given a suitable partition of the state space, called a triangulation, and values at the vertices of the triangulation. The vertex values are obtained from a Lyapunov function in a classical converse Lyapunov theorem and verification that the obtained CPA function is a Lyapunov function is shown to be equivalent to verification of several simple inequalities. Furthermore, by refining the triangulation, we show that it is always possible to construct a CPA Lyapunov function. Numerical examples are presented demonstrating the effectiveness of the proposed method.
Further data
Item Type: | Preprint, postprint |
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Additional notes (visible to public): | erscheint in:
American Control Conference (ACC), 2014. - Portland, OR, USA : IEEE , 2014 . - S. 548-553 ISBN 978-1-4799-3272-6 DOI: https://doi.org/10.1109/ACC.2014.6858660 |
Keywords: | Lyapunov methods; nonlinear control systems; asymptotic stability; linear programming; Yoshizawa construction; state-space methods; approximation methods |
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-1957-7 |
Date Deposited: | 25 Mar 2015 11:32 |
Last Modified: | 02 Jun 2021 09:59 |
URI: | https://epub.uni-bayreuth.de/id/eprint/1957 |