Title data
Hafstein, Sigurdur Freyr ; Kellett, Christopher M. ; Li, Huijuan:
Computing continuous and piecewise affine Lyapunov functions for nonlinear systems.
In: Journal of Computational Dynamics.
Vol. 2
(2015)
Issue 2
.
 pp. 227246.
ISSN 21582491
DOI: https://doi.org/10.3934/jcd.2015004
This is the latest version of this item.
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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 Alexander von HumboldtStiftung Australian Research Council 
Abstract in another language
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:  Article in a journal 

Refereed:  Yes 
Keywords:  Lyapunov function; Lyapunov methods; nonlinear systems; continuous and piecewise affine approximation 
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:  27 Jun 2016 04:50 
Last Modified:  30 Jun 2022 13:43 
URI:  https://eref.unibayreuth.de/id/eprint/33076 
Available Versions of this Item

Computing continuous and piecewise affine Lyapunov functions for nonlinear systems. (deposited 18 Apr 2015 21:00)
 Computing continuous and piecewise affine Lyapunov functions for nonlinear systems. (deposited 27 Jun 2016 04:50) [Currently Displayed]