Approximation of linear distributed parameter systems by delay systems

• Michaël Di Loreto ^[1] ; Sérine Damak ^[1] ; Damien Eberard ^[1] ; Xavier Brun ^[1]
  1. [1] Université de Lyon,France
• Localización: Automatica: A journal of IFAC the International Federation of Automatic Control, ISSN 0005-1098, Vol. 68, 2016, págs. 162-168
• Idioma: inglés
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• Resumen

  • The present work addresses continuous-time approximation of distributed parameter systems governed by linear one-dimensional partial differential equations. While approximation is usually realized by lumped systems, that is finite dimensional systems, we propose to approximate the plant by a time-delay system. Within the graph topology, we prove that, if the plant admits a coprime factorization in the algebra of BIBO-stable systems, any linear distributed parameter plant can be approximated by a time-delay system, governed by coupled differential–difference equations. Considerations on stabilization and state-space realization are carried out. A numerical method for constructive approximation is also proposed and illustrated.