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Continuous and piecewise affine Lyapunov functions using the Yoshizawa construction

Title data

Hafstein, Sigurdur Freyr ; Kellett, Christopher M. ; Li, Huijuan:
Continuous and piecewise affine Lyapunov functions using the Yoshizawa construction.
In: American Control Conference (ACC), 2014. - Portland, OR, USA : IEEE , 2014 . - pp. 548-553
ISBN 978-1-4799-3272-6
DOI: https://doi.org/10.1109/ACC.2014.6858660

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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

Abstract in another language

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: Article in a book
Refereed: Yes
Keywords: Lyapunov methods; nonlinear systems; asymptotic stability; linear programming; Yoshizawa construction; state-space methods; approximation methods
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
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 16 Apr 2015 07:37
Last Modified: 16 Apr 2015 07:37
URI: https://eref.uni-bayreuth.de/id/eprint/9502

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