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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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li_et_al_comp_contin_pwa_lyap_fct_discr_time_2015.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
Australian Research Council under Future FellowshipFT1101000746

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
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 Mar 2019 11:07
URI: https://epub.uni-bayreuth.de/id/eprint/1900

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