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Computing continuous and piecewise affine Lyapunov functions for nonlinear systems

URN to cite this document: urn:nbn:de:bvb:703-epub-2804-7

Title data

Hafstein, Sigurdur Freyr ; Kellett, Christopher M. ; Li, Huijuan:
Computing continuous and piecewise affine Lyapunov functions for nonlinear systems.
Department of Mathematics, University of Bayreuth
Bayreuth , 2016 . - 20 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 ARC Future Fellowship FT1101000746 Humboldt Research Fellowship No information
Project financing:	7. Forschungsrahmenprogramm für Forschung, technologische Entwicklung und Demonstration der Europäischen Union Alexander von Humboldt-Stiftung Australian Research Council

Abstract

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 inequalities. Numerical examples are presented demonstrating different aspects of the proposed method.

Further data

Item Type:	Preprint, postprint
Additional notes (visible to public):	erschienen in: Journal of Computational Dynamics. Bd. 2 (Juni 2015) Heft 2 . - S. 227-246. This is the 2016 revision of a paper first written in 2014
Keywords:	Lyapunov functions; continuous and piecewise affine functions; computational techniques; stability theory; ordinary differential equations
Subject classification:	2010 Mathematics Subject Classification. Primary: 93D05, 93D30, 93D20; Secondary: 93D10
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-2804-7
Date Deposited:	09 May 2016 07:32
Last Modified:	28 May 2021 06:43
URI:	https://epub.uni-bayreuth.de/id/eprint/2804