Computation of local ISS Lyapunov functions with low gains via linear programming

URN to cite this document: urn:nbn:de:bvb:703-epub-1868-6

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
Marie-Curie Initial Training Network "Sensitivity Analysis for Deterministic Controller Design" (SADCO)	264735-SADCO

Project financing:

Andere
European Union "FP7-People-ITN" programme

Abstract

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
Additional notes (visible to public):	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 input-to-state 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:703-epub-1868-6
Date Deposited:	11 Feb 2015 12:00
Last Modified:	24 Mar 2015 08:30
URI:	https://epub.uni-bayreuth.de/id/eprint/1868

Available Versions of this Item

Computation of local ISS Lyapunov functions with low gains via linear programming. (deposited 11 Feb 2015 12:00) [Currently Displayed]
- Computation of local ISS Lyapunov functions with low gains via linear programming. (deposited 27 Mar 2015 11:34)
  - Computation of local ISS Lyapunov functions with low gains via linear programming. (deposited 01 Oct 2015 10:04)

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