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 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 |
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Abstract in another language
In this paper, we present a numerical algorithm for computing ISS Lyapunov functions for continuous-time systems which are 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. The objective of the linear programming problem is to minimize the gain. We show that for every ISS system with a locally Lipschitz right-hand side our algorithm is in principle able to deliver an ISS Lyapunov function. For $C^2$ right-hand sides a more efficient algorithm is proposed.
Further data
Item Type: | Preprint, postprint |
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Additional notes: | 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. accepted for publication in DCDS-B vol. 20, no. 8 (2015) |
Keywords: | nonlinear systems; local input-to-state stability; local ISS Lyapunov function; robust Lyapunov function; linear programming |
Subject classification: | Mathematics Subject Classification Code: 37B25 93D09 93D30 (34D20 90C05 |
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: | 24 Jul 2015 10:25 |
URI: | https://eref.uni-bayreuth.de/id/eprint/6988 |
Available Versions of this Item
- Computation of local ISS Lyapunov functions with low gains via linear programming. (deposited 14 Feb 2015 22:00) [Currently Displayed]