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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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Hafstein_Kellett_Li_comp_cpa_lyap_fct_nonlin_sys_2016.pdf - Accepted Version
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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 inequalities. Numerical examples are presented demonstrating different aspects of the proposed method.

Further data

Item Type: Preprint, postprint
Additional notes (visible to public): 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 Mar 2019 11:55
URI: https://epub.uni-bayreuth.de/id/eprint/2804

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