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. 24772495.
ISSN 15313492
DOI: https://doi.org/10.3934/dcdsb.2015.20.2477
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Project information
Project title: 
Project's official title Project's id MarieCurie Initial Training Network "Sensitivity Analysis for Deterministic Controller Design" (SADCO) 264735SADCO 

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 continuoustime systems which are inputtostate 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 righthand side our algorithm is in principle able to deliver an ISS Lyapunov function. For $C^2$ righthand sides a more efficient algorithm is proposed.
Further data
Item Type:  Article in a journal 

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 inputtostate 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.unibayreuth.de/id/eprint/19439 
Available Versions of this Item

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]