The problem of reducing a system with zeros interlacing the poles (ZIP
) on the real axis is considered. It is proved that many model reducti
on methods, such as the balanced truncation, balanced residualization,
suboptimal and optimal Hankel approximations, inherit the ZIP propert
y. Properties of the Hankel singular values of ZIP systems are also li
sted. (C) 1997 Elsevier Science B.V.