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.
School of Mathematics and Physics, Chinese University of Geosciences (Wuhan), Department of Mathematics, University of Bayreuth, Fakultät für Informatik und Mathematik, Universität Passau
Bayreuth
,
2015
.  19 S.
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Project financing: 
7. Forschungsrahmenprogramm für Forschung, technologische Entwicklung und Demonstration der Europäischen Union 
Abstract
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 C² [$C^2$] righthand sides a more efficient algorithm is proposed.
Further data
Item Type:  Preprint, postprint 

Additional notes (visible to public):  erschienen in:
Discrete and Continuous Dynamical Systems. Series B. Bd. 20 (2015) Heft 8 .  S. 24772495. DOI: https://doi.org/10.3934/dcdsb.2015.20.2477 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) 
DDC Subjects:  500 Science > 510 Mathematics 
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 
Language:  English 
Originates at UBT:  Yes 
URN:  urn:nbn:de:bvb:703epub21774 
Date Deposited:  01 Oct 2015 10:04 
Last Modified:  28 May 2021 08:37 
URI:  https://epub.unibayreuth.de/id/eprint/2177 
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Computation of local ISS Lyapunov functions with low gains via linear programming. (deposited 11 Feb 2015 12:00)

Computation of local ISS Lyapunov functions with low gains via linear programming. (deposited 27 Mar 2015 11:34)
 Computation of local ISS Lyapunov functions with low gains via linear programming. (deposited 01 Oct 2015 10:04) [Currently Displayed]

Computation of local ISS Lyapunov functions with low gains via linear programming. (deposited 27 Mar 2015 11:34)