Preservation of stability under discretization of systems of ordinary differential equations

We study the stability preservation problem while passing from ordinary differential to difference equations. Using the method of Lyapunov functions, we determine the conditions under which the asymptotic stability of the zero solutions to systems of differential equations implies that the zero solu...

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Bibliographic Details
Published in:Siberian mathematical journal 2010-05, Vol.51 (3), p.383-395
Main Authors: Aleksandrov, A. Yu, Zhabko, A. P.
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
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Summary:We study the stability preservation problem while passing from ordinary differential to difference equations. Using the method of Lyapunov functions, we determine the conditions under which the asymptotic stability of the zero solutions to systems of differential equations implies that the zero solutions to the corresponding difference systems are asymptotically stable as well. We prove a theorem on the stability of perturbed systems, estimate the duration of transition processes for some class of systems of nonlinear difference equations, and study the conditions of the stability of complex systems in nonlinear approximation.
ISSN:0037-4466
1573-9260
DOI:10.1007/s11202-010-0039-y