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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Li_Hafstein_Kellett_comp_lyap_fct_discr-time_sys_using_yoshizawa_constr_2014.pdf - Accepted Version
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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
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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