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Computation of continuous and piecewise affine Lyapunov functions for discrete-time systems

Title data

Li, Huijuan ; Hafstein, Sigurdur Freyr ; Kellett, Christopher M.:
Computation of continuous and piecewise affine Lyapunov functions for discrete-time systems.
In: Journal of Difference Equations and Applications. Vol. 21 (2015) Issue 6 . - pp. 486-511.
ISSN 1023-6198
DOI: https://doi.org/10.1080/10236198.2015.1025069

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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

Project financing: Andere
European Union "FP7-People-ITN" programme; Australian Research Council

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 parameterized by the values at the vertices of the triangulation. If these vertex values satisfy system-dependent linear inequalities, the parameterized 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: Article in a journal
Refereed: Yes
Additional notes: published online: 22 April 2015
Keywords: Lyapunov theory; nonlinear systems; converse theorems; computational
methods
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics)
Profile Fields > Advanced Fields > Nonlinear Dynamics
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Profile Fields
Profile Fields > Advanced Fields
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 11 Mar 2015 11:40
Last Modified: 01 Jul 2022 10:28
URI: https://eref.uni-bayreuth.de/id/eprint/8016

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