All optimal Hankel-norm approximations and their L∞ error bounds in discrete-time †

This paper investigates a parallel problem to Glover (1984): approximate a multivariable transfer function G(z) of McMillan degree n by Ĝ(z) of McMillan degree smaller than k in discrete-time. A state-space solution is derived to the optimal Hankel-norm approximation problem, together with characterization to all optimal Hankel-norm approximations. It is shown that the L∞ error bound derived in Glover (1984) holds for discrete-time systems as well. © 2005 Taylor & Francis Group Ltd