Model reduction for linear delay systems using a delay-independent balanced truncation approach

Abstract : — A model reduction approach for asymptotically stable linear delay-differential equations is presented in this paper. Specifically, a balancing approach is developed on the basis of energy functionals that provide (bounds on) a measure of energy related to observability and controllability, respectively. The reduced-order model derived in this way is again a delay-differential equation, such that the method is structure preserving. In addition, asymptotic stability is preserved and an a priori bound on the reduction error is derived, providing a measure of accuracy of the reduction. The results are illustrated by means of application on an example.
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B. Besselink, Antoine Chaillet, N. van de Wouw. Model reduction for linear delay systems using a delay-independent balanced truncation approach. 56th IEEE Conference on Decision and Control (CDC 2017), Dec 2017, Melbourne, Australia. ⟨10.1109/CDC.2017.8264217⟩. ⟨hal-01813316⟩

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