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

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.
In: Discrete and Continuous Dynamical Systems. Series B. Vol. 20 (2015) Issue 8 . - pp. 2477-2495.
ISSN 1531-3492
DOI: https://doi.org/10.3934/dcdsb.2015.20.2477

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Project's official title
Project'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 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: Article in a journal
Refereed: Yes
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
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: 08 Oct 2015 10:44
Last Modified: 25 Jan 2017 06:55
URI: https://eref.uni-bayreuth.de/id/eprint/19439

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