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.
In: Discrete and Continuous Dynamical Systems. Series B.
Vol. 20
(2015)
Issue 8
.
- pp. 2477-2495.
ISSN 1531-3492
DOI: https://doi.org/10.3934/dcdsb.2015.20.2477
Review: |
This is the latest version of this item.
Related URLs
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 |
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Project financing: |
7. Forschungsrahmenprogramm für Forschung, technologische Entwicklung und Demonstration der Europäischen Union |
Abstract in another language
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 $C^2$ right-hand sides a more efficient algorithm is proposed.
Further data
Item Type: | Article in a journal |
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Refereed: | Yes |
Additional notes: | 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) |
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: | 08 Oct 2015 10:44 |
Last Modified: | 25 Jan 2017 06:55 |
URI: | https://eref.uni-bayreuth.de/id/eprint/19439 |
Available Versions of this Item
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Computation of local ISS Lyapunov functions with low gains via linear programming. (deposited 14 Feb 2015 22:00)
- Computation of local ISS Lyapunov functions with low gains via linear programming. (deposited 08 Oct 2015 10:44) [Currently Displayed]