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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-1962-5

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 , 2014 . - 20 S.

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Project information

Project title:
Project's official titleProject's id
Marie-Curie Initial Training Network "Sensitivity Analysis for Deterministic Controller Design" (SADCO)264735-SADCO
ARC Future FellowshipFT1101000746
Humboldt Research FellowshipNo 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 linear inequalities. A numerical example is provided to illustrate the advantages of the proposed technique.

Further data

Item Type: Preprint, postprint
Additional notes (visible to public): The first version of this paper was updated in January 2015.
Keywords: Lyapunov function; Lyapunov methods; nonlinear systems; continuous and piecewise affine approximation
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-1962-5
Date Deposited: 17 Apr 2015 06:41
Last Modified: 28 Mar 2019 11:53
URI: https://epub.uni-bayreuth.de/id/eprint/1962

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