at Google ScholarTitle data
Li, Huijuan ; Hafstein, Sigurdur Freyr ; Kellett, Christopher M.:
Computation of continuous and piecewise affine Lyapunov functions for discrete-time systems.
Department of Mathematics, University of Bayreuth
Bayreuth
,
2015
. - 24 p.
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 Australian Research Council under Future Fellowship FT1101000746 |
|---|
Abstract in another language
In this paper, we present a new approach for computing Lyapunov functions for nonlinear discrete-time systems with an asymptotically stable equilibrium at the origin. Given a suitable triangulation of a compact neighbourhood of the origin, a continuous and piecewise affine function can be parameterised by the values at the vertices of the triangulation. If these vertex values satisfy system-dependent linear inequalities, the parameterised function
is a Lyapunov function for the system. We propose calculating these vertex values using constructions from two classical converse Lyapunov theorems originally due to Yoshizawa and Massera. Numerical examples are presented to illustrate the proposed approach.
Further data
| Item Type: | Preprint, postprint |
|---|---|
| Keywords: | Lyapunov theory; nonlinear systems; converse theorems; computational 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: | 07 Mar 2015 22:00 |
| Last Modified: | 09 Mar 2015 11:08 |
| URI: | https://eref.uni-bayreuth.de/id/eprint/7994 |
Available Versions of this Item
- Computation of continuous and piecewise affine Lyapunov functions for discrete-time systems. (deposited 07 Mar 2015 22:00) [Currently Displayed]