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

Title data

Li, Huijuan ; Grüne, Lars:
Computation of Local ISS Lyapunov Functions for Discrete-time Systems Via Linear Programming.
In: Journal of Mathematical Analysis and Applications. Vol. 438 (March 2016) Issue 2 . - pp. 701-719.
ISSN 0022-247X
DOI: https://doi.org/10.1016/j.jmaa.2016.01.045

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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
Fundamental Research Funds for the Central Universities, China University of Geosciences, WuhanCUG160603

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

Abstract in another language

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: Article in a journal
Refereed: Yes
Additional notes: 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)
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
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 07 Mar 2016 10:21
Last Modified: 30 Mar 2016 07:27
URI: https://eref.uni-bayreuth.de/id/eprint/31364

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