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

DOI10.1063/1.3241391zbMATH Open1181.93069arXiv0811.0061OpenAlexW1572251010MaRDI QIDQ5851474

Iasson Karafyllis, Lars Grüne

Publication date: 22 January 2010

Published in: AIP Conference Proceedings (Search for Journal in Brave)

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 exploited and numerous illustrating applications are presented for systems with a globally asymptotically stable equilibrium point. The obtained results can be used for the control of the global discretization error as well.

Full work available at URL: https://arxiv.org/abs/0811.0061

zbMATH Keywords

feedback stabilizationnonlinear systemsdifferential equationsnonlinear acousticsnumerical analysisstability of numerical schemes

Mathematics Subject Classification ID

Stabilization of systems by feedback (93D15) Nonlinear systems in control theory (93C10) Linear systems in control theory (93C05) Hydro- and aero-acoustics (76Q05) Control/observation systems governed by ordinary differential equations (93C15)

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