Balanced realisation and Hankel-norm approximation of systems involving delays

Approximation of the transfer functions G(s)e-ST (with G(s) rational) is considered via the singular values, ??i, of its Hankel operator. It is first shown how to calculate ??i and the corresponding Schmidt vectors for this class of transfer functions. Then bounds on the singular values of more general Hankel operators are derived and this gives asymptotic estimates for the ??i above. The results can be used to construct balanced realisations or Hankel norm approximations.