at Google ScholarTitle 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 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 ARC Future Fellowship FT1101000746 Humboldt Research Fellowship No information |
|---|
Abstract in another language
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 |
|---|---|
| Keywords: | Lyapunov methods; nonlinear control systems; asymptotic stability; linear programming; Yoshizawa construction; state-space methods; 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: | 28 Mar 2015 22:00 |
| Last Modified: | 30 Mar 2015 07:14 |
| URI: | https://eref.uni-bayreuth.de/id/eprint/9469 |
Available Versions of this Item
- Continuous and piecewise affine Lyapunov functions using the Yoshizawa construction. (deposited 28 Mar 2015 22:00) [Currently Displayed]