Model reduction for a class of nonlinear delay differential equations with time-varying delays

Conference paper (2015)

Authors

N. van de Wouw Team Bart De Schutter - Mechanical, Maritime and Materials Engineering , University of Minnesota System, Eindhoven University of Technology
Wim Michiels Katholieke Universiteit Leuven
Bart Besselink KTH Royal Institute of Technology
Research Group
Team Bart De Schutter (Mechanical, Maritime and Materials Engineering) (TU Delft)
Differential equations Stability analysis Mathematical model Delays Reduced order systems Asymptotic stability Delay systems
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Published Date

2015

Language

English

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Faculty

Mechanical, Maritime and Materials Engineering

Department

Delft Center for Systems and Control

Research Group

Team Bart De Schutter

Abstract

In this paper, a structure-preserving model reduction approach for a class of nonlinear delay differential equations with time-varying delays is proposed. Benefits of this approach are, firstly, the fact that the delay nature of the system is preserved after reduction, secondly, that input-output stability properties are preserved and, thirdly, that a computable error bound reflecting the accuracy of the reduction is provided. These results are also applicable to large-scale linear delay differential equations with constant delays. The effectiveness of the results is evidenced by means of an illustrative example involving the nonlinear delayed dynamics of the turning process.