Feedback stabilization methods for the numerical solution of ordinary differential equations

DOI zum Zitieren der Version auf EPub Bayreuth: https://doi.org/10.15495/EPub_UBT_00005627
URN to cite this document: urn:nbn:de:bvb:703-epub-5627-9

Title data

Karafyllis, Iasson ; Grüne, Lars:
Feedback stabilization methods for the numerical solution of ordinary differential equations.
Bayreuth , 2010

	Format: PDF Name: gruene_et_al_dcds-b_2009.pdf Version: Published Version Available under License Creative Commons BY 4.0: Attribution
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Abstract

In this work we study the problem of step size selection for numerical schemes, which guarantees that the numerical solution presents the same qualitative behavior as the original system of ordinary differential equations, by means of tools from nonlinear control theory. Lyapunov-based and Small-Gain feedback stabilization methods are presented for systems with a globally asymptotically stable equilibrium point. Proceeding this way, we derive conditions under which the step size selection problem is solvable (including a nonlinear generalization of the well-known A-stability property for the implicit Euler scheme) as well as step size selection strategies for several applications.

Further data

Item Type:	Preprint, postprint
Additional notes (visible to public):	erscheint in: Discrete and Continuous Dynamical Systems - Series B. Bd. 16 (2011) Heft 1 . - S. 283-317 DOI: https://doi.org/10.3934/dcdsb.2011.16.283
Keywords:	stability of numerical approximations; feedback stabilization; nonlinear systems
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-5627-9
Date Deposited:	26 May 2021 13:14
Last Modified:	08 Jun 2021 10:25
URI:	https://epub.uni-bayreuth.de/id/eprint/5627

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