at Google ScholarTitle 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 p.
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 |
|---|
Abstract in another language
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: | Mathematics Subject Classification Code: 93D30 (34D20 93C10). 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 |
| 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: | 14 Feb 2015 22:00 |
| Last Modified: | 16 Feb 2015 12:54 |
| URI: | https://eref.uni-bayreuth.de/id/eprint/6990 |
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