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Computation of local ISS Lyapunov functions via linear programming

Title data

Li, Huijuan ; Baier, Robert ; Grüne, Lars ; Hafstein, Sigurdur Freyr ; Wirth, Fabian:
Computation of local ISS Lyapunov functions via linear programming.
In: MTNS 2014 : Proceedings on the 21st International Symposium on Mathematical Theory of Networks and Systems, July 7--11, 2014, University of Groningen. - Groningen, The Netherlands , 2014 . - pp. 1189-1195
ISBN 978-90-367-6321-9

This is the latest version of this item.

Official URL: Volltext

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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: European Union "FP7-People-ITN" programme

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: Article in a book
Refereed: Yes
Additional notes: Paper No. 158, full paper.

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
Subject classification: Mathematics Subject Classification Code: 93D30 (34D20 93C10)
Institutions of the University: 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 > Advanced Fields > Nonlinear Dynamics
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)
Profile Fields
Profile Fields > Advanced Fields
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 02 Mar 2015 09:45
Last Modified: 23 Mar 2015 12:23
URI: https://eref.uni-bayreuth.de/id/eprint/7724

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