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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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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
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
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: 28 Mar 2019 11:51
URI: https://epub.uni-bayreuth.de/id/eprint/1957

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