Computation of Local ISS Lyapunov Functions for Discrete-time Systems Via Linear Programming

URN to cite this document: urn:nbn:de:bvb:703-epub-2735-3

Title data

Li, Huijuan ; Grüne, Lars:
Computation of Local ISS Lyapunov Functions for Discrete-time Systems Via Linear Programming.
School of Mathematics and Physics, Chinese University of Geosciences (Wuhan), Department of Mathematics, University of Bayreuth
Bayreuth , 2016 . - 29 S.

Format:	PDF
Name:	ISS LYF for DTSYS - revision - final.pdf
Version:	Preprint
Available under License	German copyright law. This contribution is freely accessible with the consent of the copyright holder on the basis of an (DFG-funded) alliance or national license. 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
Fundamental Research Funds for the Central Universities, China University of Geosciences, Wuhan	CUG160603

Project financing:

7. Forschungsrahmenprogramm für Forschung, technologische Entwicklung und Demonstration der Europäischen Union

Abstract

This paper presents a numerical algorithm for computing ISS Lyapunov functions for discrete-time systems which are input-to-state stable (ISS) on compact subsets of the state space. The algorithm relies on solving a linear optimization problem and delivers a continuous and piecewise affine ISS Lyapunov function on a suitable triangulation covering the given compact set excluding a small neighbourhood of the origin. The objective of the linear optimization problem is to minimize the ISS gain. It is shown that for every ISS system there exist a suitable triangulation such that the proposed algorithm terminates successfully.

Further data

Item Type:	Preprint, postprint
Additional notes (visible to public):	erschienen in: Journal of Mathematical Analysis and Applications. Bd. 438 (März 2016) Heft 2 . - S. 701-719. DOI: https://doi.org/10.1016/j.jmaa.2016.01.045
Keywords:	discrete-time systems; local input-to-state stability; local ISS Lyapunov function; Lyapunov function; linear programming
Subject classification:	Mathematics Subject Classification Code: 37B25 93D09 93D30 (90C05)
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) Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics) > Chair Mathematics V (Applied Mathematics) - Univ.-Prof. Dr. Lars Grüne 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-2735-3
Date Deposited:	04 Feb 2016 08:35
Last Modified:	28 May 2021 06:54
URI:	https://epub.uni-bayreuth.de/id/eprint/2735

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