Title data
Hafstein, Sigurdur Freyr ; Kellett, Christopher M. ; Li, Huijuan:
Continuous and piecewise affine Lyapunov functions using the Yoshizawa construction.
In:
American Control Conference (ACC), 2014. 
Portland, OR, USA
: IEEE
,
2014
.  pp. 548553
ISBN 9781479932726
DOI: https://doi.org/10.1109/ACC.2014.6858660
This is the latest version of this item.
Related URLs
Project information
Project title: 
Project's official title Project's id MarieCurie Initial Training Network "Sensitivity Analysis for Deterministic Controller Design" (SADCO) 264735SADCO ARC Future Fellowship FT1101000746 Humboldt Research Fellowship No information 

Project financing: 
7. Forschungsrahmenprogramm für Forschung, technologische Entwicklung und Demonstration der Europäischen Union 
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:  Article in a book 

Refereed:  Yes 
Keywords:  Lyapunov methods; nonlinear systems; asymptotic stability; linear programming; Yoshizawa construction; statespace 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:  16 Apr 2015 07:37 
Last Modified:  16 Apr 2015 07:37 
URI:  https://eref.unibayreuth.de/id/eprint/9502 
Available Versions of this Item

Continuous and piecewise affine Lyapunov functions using the Yoshizawa construction. (deposited 28 Mar 2015 22:00)
 Continuous and piecewise affine Lyapunov functions using the Yoshizawa construction. (deposited 16 Apr 2015 07:37) [Currently Displayed]