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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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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

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
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: 28 Mar 2019 11:52
URI: https://epub.uni-bayreuth.de/id/eprint/1958

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