A projection approach for model reduction of large-scale time-delay systems, with application to a boundary controlled PDE

We present a model order reduction method which allows the construction of a reduced, delay free model of a given dimension for linear time-delay systems. The method builds on the equivalent representation of the time-delay system as an infinite-dimensional linear problem. It combines ideas from a finite-dimensional approximation via a spectral discretization on the one hand, and a Krylov-Padé model reduction approach on the other hand. The method exhibits a good spectral approximation of the original model, in the sense that the smallest characteristic roots are well approximated and the non-converged eigenvalues of the reduced model have a favorable location, and it preserves moments at zero and at infinity. The model reduction approach is illustrated by means of a PDE model for a heated rod with delay in the boundary control.