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 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 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

Available Versions of this Item

Computation of Local ISS Lyapunov Functions for Discrete-time Systems Via Linear Programming. (deposited 06 Feb 2016 22:00)
- Computation of Local ISS Lyapunov Functions for Discrete-time Systems Via Linear Programming. (deposited 07 Mar 2016 10:21) [Currently Displayed]