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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
,
2016
. - 20 S.
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Project information
| Project title: |
Project's official title Project's id SADCO - Sensitivity Analysis for Deterministic Controller Design 264735 |
|---|---|
| Project financing: |
7. Forschungsrahmenprogramm für Forschung, technologische Entwicklung und Demonstration der Europäischen Union Alexander von Humboldt-Stiftung Australian Research Council Marie Curie Initial Training Network |
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 inequalities. Numerical examples are presented demonstrating different aspects of the proposed method.
Further data
| Item Type: | Preprint, postprint |
|---|---|
| Additional notes (visible to public): | erschienen in:
Journal of Computational Dynamics. Bd. 2 (Juni 2015) Heft 2 . - S. 227-246. This is the 2016 revision of a paper first written in 2014 |
| Keywords: | Lyapunov functions; continuous and piecewise affine functions; computational
techniques; stability theory; ordinary differential equations |
| Subject classification: | 2010 Mathematics Subject Classification. Primary: 93D05, 93D30, 93D20; Secondary: 93D10 |
| 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-2804-7 |
| Date Deposited: | 09 May 2016 07:32 |
| Last Modified: | 15 Dec 2025 14:38 |
| URI: | https://epub.uni-bayreuth.de/id/eprint/2804 |
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