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

URN to cite this document: urn:nbn:de:bvb:703-epub-2177-4

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.
School of Mathematics and Physics, Chinese University of Geosciences (Wuhan), Department of Mathematics, University of Bayreuth, Fakultät für Informatik und Mathematik, Universität Passau
Bayreuth , 2015 . - 19 S.

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Project information

Project title:
Project's official titleProject's id
Marie-Curie Initial Training Network "Sensitivity Analysis for Deterministic Controller Design" (SADCO)264735-SADCO

Project financing: 7. Forschungsrahmenprogramm für Forschung, technologische Entwicklung und Demonstration der Europäischen Union

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 C² [$C^2$] right-hand sides a more efficient algorithm is proposed.

Further data

Item Type: Preprint, postprint
Additional notes (visible to public): This paper appeared in Discrete Contin. Dyn. Syst. Ser. B. 20(8) (2015).

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-2177-4
Date Deposited: 01 Oct 2015 10:04
Last Modified: 28 Mar 2019 15:08
URI: https://epub.uni-bayreuth.de/id/eprint/2177

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