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

URN to cite this document: urn:nbn:de:bvb:703-epub-1900-1

Title 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 S.

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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 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
Additional notes (visible to public):	erschienen in: Journal of Difference Equations and Applications. (2015) . - S. 1-24. DOI: https://doi.org/10.1080/10236198.2015.1025069
Keywords:	Lyapunov theory; nonlinear systems; converse theorems; computational methods
DDC Subjects:	500 Science > 510 Mathematics
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
Language:	English
Originates at UBT:	Yes
URN:	urn:nbn:de:bvb:703-epub-1900-1
Date Deposited:	04 Mar 2015 11:23
Last Modified:	28 May 2021 10:02
URI:	https://epub.uni-bayreuth.de/id/eprint/1900

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