Model reduction for delay differential equations with guaranteed stability and error bound

• Nathan van de Wouw ^[1] ; Wim Michiels ^[2] ; Bart Besselink ^[3]
  1. [1] Eindhoven University of Technology

     Eindhoven University of Technology

     Países Bajos

     
  2. [2] KU Leuven

     KU Leuven

     Arrondissement Leuven, Bélgica

     
  3. [3] School of Electrical Engineering, Stockholm, Sweden

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• Localización: Automatica: A journal of IFAC the International Federation of Automatic Control, ISSN 0005-1098, Vol. 55, 2015, págs. 132-139
• Idioma: inglés
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• Resumen

  • In this paper, a structure-preserving model reduction approach for a class of delay differential equations 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 applicable to large-scale linear delay differential equations with constant delays, but also extensions to a class of nonlinear delay differential equations with time-varying delays are presented. The effectiveness of the results is evidenced by means of an illustrative example.