Computation of Lyapunov functions for discrete-time systems using the Yoshizawa construction

URN to cite this document: urn:nbn:de:bvb:703-epub-1958-2

Title data

Li, Huijuan ; Hafstein, Sigurdur Freyr ; Kellett, Christopher M.:
Computation of Lyapunov functions for discrete-time systems using the Yoshizawa construction.
Department of Mathematics, University of Bayreuth
Bayreuth, Germany , 2014 . - 7 S.

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Name:	Li_Hafstein_Kellett_comp_lyap_fct_discr-time_sys_using_yoshizawa_constr_2014.pdf
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Available under License	German copyright law. This contribution is freely accessible with the consent of the copyright holder on the basis of an (DFG-funded) alliance or national license. The document may be used free of charge for personal use. In addition, the reproduction, editing, distribution and any kind of exploitation require the written consent of the respective rights holder.

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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
Australian Research Council; Alexander von Humboldt Foundation

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. The proposed method constructs a continuous piecewise affine (CPA) function on a compact subset of the state space containing the origin, given a suitable triangulation or partition of the compact set and values at the vertices of the triangulation. Here, the vertex values are fixed using a function from a classical converse Lyapunov theorem originally due to Yoshizawa. Several numerical examples are presented to illustrate the proposed approach.

Further data

Item Type:	Preprint, postprint
Additional notes (visible to public):	erschienen in: Proceedings of the IEEE 53rd Annual Conference on Decision and Control Held in Los Angeles, California, 2014. - Los Angeles, CA, USA : Institute of Electrical and Electronics Engineers (IEEE) , 2014 . - S. 5512-5517 ISBN 978-1-4799-7746-8 DOI: https://doi.org/10.1109/CDC.2014.7040251
Keywords:	Lyapunov methods; nonlinear control systems; asymptotic stability; linear programming; Yoshizawa construction; discrete-time systems
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-1958-2
Date Deposited:	25 Mar 2015 11:37
Last Modified:	01 Jun 2021 09:25
URI:	https://epub.uni-bayreuth.de/id/eprint/1958

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