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Approximation of linear distributed parameter systems by delay systems

Abstract : 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.
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Michaël Di Loreto, Sérine Damak, Damien Eberard, Xavier Brun. Approximation of linear distributed parameter systems by delay systems. Automatica, Elsevier, 2016, 68, pp.162-168. ⟨10.1016/j.automatica.2016.01.065⟩. ⟨hal-01281589⟩

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