Feedback Stabilization Methods for the Numerical Solution of Systems of Ordinary Differential Equations

DOI zum Zitieren der Version auf EPub Bayreuth: https://doi.org/10.15495/EPub_UBT_00005583
URN to cite this document: urn:nbn:de:bvb:703-epub-5583-4

Title data

Karafyllis, Iasson ; Grüne, Lars:
Feedback Stabilization Methods for the Numerical Solution of Systems of Ordinary Differential Equations.
Bayreuth , 2009

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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):	erschienen In: Numerical analysis and applied mathematics : International Conference on Numerical Analysis and Applied Mathematics 2009. - Melville, NY : American Inst. of Physics , 2009 . - S. 152-155
Keywords:	Stability of numerical schemes; 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-5583-4
Date Deposited:	20 May 2021 12:44
Last Modified:	20 May 2021 12:45
URI:	https://epub.uni-bayreuth.de/id/eprint/5583

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