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Continuous and piecewise affine Lyapunov functions using the Yoshizawa construction

URN to cite this document: urn:nbn:de:bvb:703-epub-1957-7

Title data

Hafstein, Sigurdur Freyr ; Kellett, Christopher M. ; Li, Huijuan:
Continuous and piecewise affine Lyapunov functions using the Yoshizawa construction.
Department of Mathematics, University of Bayreuth
Bayreuth , 2013 . - 6 S.

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Available under License	German copyright law. 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

We present a novel numerical technique for the computation of a Lyapunov function for nonlinear systems with an asymptotically stable equilibrium point. Our proposed approach constructs a continuous piecewise affine (CPA) function given a suitable partition of the state space, called a triangulation, and values at the vertices of the triangulation. The vertex values are obtained from a Lyapunov function in a classical converse Lyapunov theorem and verification that the obtained CPA function is a Lyapunov function is shown to be equivalent to verification of several simple inequalities. Furthermore, by refining the triangulation, we show that it is always possible to construct a CPA Lyapunov function. Numerical examples are presented demonstrating the effectiveness of the proposed method.

Further data

Item Type:	Preprint, postprint
Additional notes (visible to public):	erscheint in: American Control Conference (ACC), 2014. - Portland, OR, USA : IEEE , 2014 . - S. 548-553 ISBN 978-1-4799-3272-6 DOI: https://doi.org/10.1109/ACC.2014.6858660
Keywords:	Lyapunov methods; nonlinear control systems; asymptotic stability; linear programming; Yoshizawa construction; state-space methods; approximation 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-1957-7
Date Deposited:	25 Mar 2015 11:32
Last Modified:	02 Jun 2021 09:59
URI:	https://epub.uni-bayreuth.de/id/eprint/1957

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