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Title data
Li, Huijuan ; Baier, Robert ; Grüne, Lars ; Hafstein, Sigurdur Freyr ; Wirth, Fabian:
Computation of local ISS Lyapunov functions via linear programming.
Department of Mathematics, University of Bayreuth
Bayreuth
,
2014
. - 7 S.
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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: |
Andere European Union "FP7-People-ITN" programme |
Abstract
In this paper, we present a numerical algorithm for computing a local ISS Lyapunov function for systems which are locally 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. We show that the ISS Lyapunov function delivered by the algorithm is a viscosity subsolution of a partial differential equation.
Further data
| Item Type: | Preprint, postprint |
|---|---|
| Additional notes (visible to public): | 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 input-to-state stability; local ISS Lyapunov function; linear programming; viscosity subsolution |
| Subject classification: | Mathematics Subject Classification Code: 93D30 (34D20 93C10) |
| 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:703-epub-1880-3 |
| Date Deposited: | 11 Feb 2015 11:49 |
| Last Modified: | 28 Mar 2019 11:03 |
| URI: | https://epub.uni-bayreuth.de/id/eprint/1880 |
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