Title data
Li, Huijuan ; Baier, Robert ; Grüne, Lars ; Hafstein, Sigurdur Freyr ; Wirth, Fabian:
Computation of local ISS Lyapunov functions via linear programming.
In:
MTNS 2014 : Proceedings on the 21st International Symposium on Mathematical Theory of Networks and Systems, July 711, 2014, University of Groningen. 
Groningen, The Netherlands
,
2014
.  pp. 11891195
ISBN 9789036763219
This is the latest version of this item.
Related URLs
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: 
European Union "FP7PeopleITN" programme 
Abstract in another language
In this paper, we present a numerical algorithm for computing a local ISS Lyapunov function for systems which are locally 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. We show that the ISS Lyapunov function delivered by the algorithm is a viscosity subsolution of a partial differential equation.
Further data
Item Type:  Article in a book 

Refereed:  Yes 
Additional notes:  Paper No. 158, full paper.
Contents: I. Introduction II. Notations and preliminaries III. The algorithm III.A Definitions III.B Interpolation errors III.C The algorithm IV. Main result © 2014 IEEE. Reuse of this content is subject to the IEEE Copyright. This content will be published in: Proceedings on the 21st International Symposium on Mathematical Theory of Networks and Systems (MTNS 2014), July 7–11, 2014, University of Groningen, Groningen, Netherlands, check the forthcoming abstract in IEEE Explore. 
Keywords:  nonlinear systems; local inputtostate stability; local ISS Lyapunov function; linear programming; viscosity subsolution 
Subject classification:  Mathematics Subject Classification Code: 93D30 (34D20 93C10) 
Institutions of the University:  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 > Advanced Fields > Nonlinear Dynamics 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) Profile Fields Profile Fields > Advanced Fields 
Result of work at the UBT:  Yes 
DDC Subjects:  500 Science > 510 Mathematics 
Date Deposited:  02 Mar 2015 09:45 
Last Modified:  01 Jun 2021 09:52 
URI:  https://eref.unibayreuth.de/id/eprint/7724 
Available Versions of this Item

Computation of local ISS Lyapunov functions via linear programming. (deposited 14 Feb 2015 22:00)
 Computation of local ISS Lyapunov functions via linear programming. (deposited 02 Mar 2015 09:45) [Currently Displayed]