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Computation of local ISS Lyapunov functions via linear programming

URN to cite this document: urn:nbn:de:bvb:703-epub-1880-3

Title data

Li, Huijuan ; Baier, Robert ; Grüne, Lars ; Hafstein, Sigurdur Freyr ; Wirth, Fabian:
Computation of local ISS Lyapunov functions via linear programming.
Department of Mathematics, University of Bayreuth
Bayreuth , 2014 . - 7 S.

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Li_Baier_Gruene_et_al_iss_lyap_fct_mtns_2014.pdf - Accepted Version
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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: Andere
European Union "FP7-People-ITN" programme

Abstract

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: Preprint, postprint
Additional notes (visible to public): 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)
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-1880-3
Date Deposited: 11 Feb 2015 11:49
Last Modified: 28 Mar 2019 11:03
URI: https://epub.uni-bayreuth.de/id/eprint/1880

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