  We analyze a structure-preserving model order reduction technique for delay
and stochastic delay equations based on the balanced truncation method and
provide a system theoretic interpretation. Transferring error bounds based on
Hankel operators to delay systems, we find error estimates for the difference
between the dynamics of the full and reduced model. This analysis also yields
new error bounds for bilinear systems and stochastic systems with
multiplicative noise and non-zero initial states.
