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Linear programming based Lyapunov function computation for differential inclusions

Title data

Baier, Robert ; Grüne, Lars ; Freyr Hafstein, Sigurđur:
Linear programming based Lyapunov function computation for differential inclusions.
In: Discrete and Continuous Dynamical Systems. Series B. Vol. 17 (2012) Issue 1 . - pp. 33-56.
ISSN 1531-3492
DOI: https://doi.org/10.3934/dcdsb.2012.17.33

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Abstract in another language

We present a numerical algorithm for computing Lyapunov functions for a class of strongly asymptotically stable nonlinear differential inclusions which includes spatially switched systems and systems with uncertain parameters. The method relies on techniques from nonsmooth analysis and linear programming and constructs a piecewise affine Lyapunov function. We provide necessary background material from nonsmooth analysis and a thorough analysis of the method which in particular shows that whenever a Lyapunov function exists then the algorithm is in principle able to compute it. Two numerical examples illustrate our method.

Further data

Item Type: Article in a journal
Refereed: Yes
Additional notes: CONTENTS:
1. Introduction
2. Notation and preliminaries
3. Lyapunov functions
4. The algorithm
5. Examples
Keywords: switched systems; stability of nonlinear systems; piecewise affine functions; invariance principle; Lyapunov functions; numerical construction of Lyapunov functions; differential inclusions
Subject classification: Mathematics Subject Classification Code: 93D30 93D20 (34D20 34A60 34A36)
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
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)
Result of work at the UBT: Yes
DDC Subjects: 500 Science
Date Deposited: 22 Feb 2021 12:36
Last Modified: 29 Mar 2021 07:09
URI: https://eref.uni-bayreuth.de/id/eprint/63243