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Linear programming based Lyapunov function computation for differential inclusions

DOI zum Zitieren der Version auf EPub Bayreuth: https://doi.org/10.15495/EPub_UBT_00005635
URN to cite this document: urn:nbn:de:bvb:703-epub-5635-3

Title data

Baier, Robert ; Grüne, Lars ; Freyr Hafstein, Sigurđur:
Linear programming based Lyapunov function computation for differential inclusions.
Bayreuth , 2012

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Abstract

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: Preprint, postprint
Additional notes (visible to public): erscheint in:
Discrete and Continuous Dynamical Systems. Series B. Bd. 17 (2012) Heft 1 . - S. 33-56
Keywords: switched systems; stability of nonlinear systems; piecewise affine functions; invariance principle; Lyapunov functions; numerical construction of Lyapunov functions; differential inclusions
DDC Subjects: 500 Science
500 Science > 510 Mathematics
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)
Language: English
Originates at UBT: Yes
URN: urn:nbn:de:bvb:703-epub-5635-3
Date Deposited: 28 May 2021 10:21
Last Modified: 07 Jun 2021 10:58
URI: https://epub.uni-bayreuth.de/id/eprint/5635

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