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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.
![[thumbnail of ISS LYF for DTSYS - revision - final.pdf]](https://epub.uni-bayreuth.de/style/images/fileicons/application_pdf.png) |
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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 |
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| 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.
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