Improved stable approximants using the Routh array

A simple method for obtaining a stable reduced-order (
k
th-order) approximant
G_{k}(s)
for a stable hlgh-order (
n
th-order) transfer function
G(s)
is described. The method is an improvement over some previous methods [1], [2] in that it not only ensures matching of the first
k
time moments of
G(s)
and
G_{k}(s)
, but it also ensures that the (
k+1
)th time moment of
G_{k}(s)
be as close as possible to the corresponding value in
G(s)
.