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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.
Department of Mathematics, University of Bayreuth
Bayreuth , 2015 . - 19 p.

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Official URL: Volltext

Project information

Project title:
Project's official titleProject'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 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: Preprint, postprint, working paper, discussion paper
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.
accepted for publication in DCDS-B vol. 20, no. 8 (2015)
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: 14 Feb 2015 22:00
Last Modified: 24 Jul 2015 10:25
URI: https://eref.uni-bayreuth.de/id/eprint/6988

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