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.
Department of Mathematics, University of Bayreuth
Bayreuth
,
2015
.  19 S.


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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 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):  This paper is accepted and will appear in Discrete Contin. Dyn. Syst. Ser. B.
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:703epub19810 
Date Deposited:  27 Mar 2015 11:34 
Last Modified:  27 Mar 2015 11:34 
URI:  https://epub.unibayreuth.de/id/eprint/1981 
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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) [Currently Displayed]