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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.
Department of Mathematics, University of Bayreuth
Bayreuth , 2014 . - 7 p.

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Official URL: Volltext

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

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: Preprint, postprint
Additional notes: Mathematics Subject Classification Code: 93D30 (34D20 93C10).

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
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: 14 Feb 2015 22:00
Last Modified: 16 Feb 2015 12:54
URI: https://eref.uni-bayreuth.de/id/eprint/6990

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