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Title data
Hafstein, Sigurdur Freyr ; Kellett, Christopher M. ; Li, Huijuan:
Computing continuous and piecewise affine Lyapunov functions for nonlinear systems.
Department of Mathematics, University of Bayreuth
Bayreuth
,
2014
. - 20 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 |
|---|---|
| Project financing: |
7. Forschungsrahmenprogramm für Forschung, technologische Entwicklung und Demonstration der Europäischen Union Alexander von Humboldt-Stiftung Australian Research Council |
Abstract
We present a numerical technique for the computation of a Lyapunov function for nonlinear systems with an asymptotically stable equilibrium point. The proposed approach constructs a partition of the state space, called a triangulation, and then computes values at the vertices of the triangulation using a Lyapunov function from a classical converse Lyapunov theorem due to Yoshizawa. A simple interpolation of the vertex values then yields a Continuous and Piecewise Affine (CPA) function. Verification that the obtained CPA function is a Lyapunov function is shown to be equivalent to verification of several simple linear inequalities. A numerical example is provided to illustrate the advantages of the proposed technique.
Further data
| Item Type: | Preprint, postprint |
|---|---|
| Additional notes (visible to public): | The first version of this paper was updated in January 2015. |
| Keywords: | Lyapunov function; Lyapunov methods; nonlinear systems; continuous and piecewise affine approximation |
| 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-1962-5 |
| Date Deposited: | 17 Apr 2015 06:41 |
| Last Modified: | 28 Mar 2019 11:53 |
| URI: | https://epub.uni-bayreuth.de/id/eprint/1962 |
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