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

Conference paper (2015)

Authors

N. van de Wouw Eindhoven University of Technology, University of Minnesota System,

Wim Michiels Katholieke Universiteit Leuven

Bart Besselink KTH Royal Institute of Technology

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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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.