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.

PDF ISS LYF for DTSYS - revision - final.pdf - Preprint Available under License Deutsches Urheberrechtsgesetz . Download (511kB)

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):	Accepted for publication in the Journal of Mathematical Analysis and Applications
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 Mar 2019 14:50
URI:	https://epub.uni-bayreuth.de/id/eprint/2735

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