Model Reduction For Linear Delay Systems Using A Delay-Independent Balanced Truncation Approach

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.