Login
Publications by the same author
plus in the repository
plus in Google Scholar
Bibliografische Daten exportieren		  

Computation of local ISS Lyapunov functions with low gains via linear programming

URN to cite this document: urn:nbn:de:bvb:703-epub-1981-0

Title data

Li, Huijuan ; Baier, Robert ; Grüne, Lars ; Hafstein, Sigurdur Freyr ; Wirth, Fabian:
Computation of local ISS Lyapunov functions with low gains via linear programming.
Department of Mathematics, University of Bayreuth
Bayreuth , 2015 . - 19 S.

Warning
There is a more recent version of this item available.

[thumbnail of Li_Baier_Gruene_et_al_comp_local_iss_lyap_fct_low_gains_mar_2015.pdf]
Format: PDF
Name: Li_Baier_Gruene_et_al_comp_local_iss_lyap_fct_low_gains_mar_2015.pdf
Version: Accepted Version
Available under License German copyright law. 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.
Download (600kB)

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

Abstract

In this paper, we present a numerical algorithm for computing ISS Lyapunov functions for continuous-time systems which are input-to-state stable (ISS) on compact subsets of the state space. The algorithm relies on a linear programming problem and computes a continuous piecewise affine ISS Lyapunov function on a simplicial grid covering the given compact set excluding a small neighborhood of the origin. The objective of the linear programming problem is to minimize the gain. We show that for every ISS system with a locally Lipschitz right-hand side our algorithm is in principle able to deliver an ISS Lyapunov function. For C² [$C^2$] right-hand sides a more efficient algorithm is proposed.

Further data

Item Type: Preprint, postprint
Additional notes (visible to public): This paper is accepted and will appear in Discrete Contin. Dyn. Syst. Ser. B.

Contents:
1. Introduction
2. Notations and Preliminaries
3. The algorithm
3.1 Definitions
3.2 Interpolation errors
3.3 The Algorithm
4. Main results
5. Examples
6. Conclusions
7. Acknowledgement
Keywords: nonlinear systems; local input-to-state stability; local ISS Lyapunov function; robust Lyapunov function; linear programming
Subject classification: Mathematics Subject Classification Code: 37B25 93D09 93D30 (34D20 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-1981-0
Date Deposited: 27 Mar 2015 11:34
Last Modified: 27 Mar 2015 11:34
URI: https://epub.uni-bayreuth.de/id/eprint/1981

Available Versions of this Item

Download Statistics

Downloads

Downloads per month over past year