 
Summary: 502 IEEE TRANSACTIONS ON AUTOMATIC CONTROL, VOL. 35, NO. 4, APRIL 1990
100"103 102 101 100 101 102 103
rad/sec
Fig 1 Optimal Hankel MDA, 10state MlMO example
H(s)determined by (lo), or equivalently by (46), differs slightly from
the H(s)in Glover's Theorem 8.7, including in effect an extra feedback
around K which, as shown in (33)(39), implicitly replaces K by a K
which satisfies the Glover constraint C2 +K(s)B: = 0. Consequently,
the descriptor representation of Theorem 1 takes the same simple form
in both optimal (p = u k + , ) and suboptimal (uk > p > Q + , ) cases. The
price one pays for this increased simplicity is that, in the optimal case
p = ukfl, there is a certain amount of redundancy in the matrix K ( s )
of Theorem 1, the effective dimension of the matrix K ( s )being reduced
by the multiplicity of U ~ + I~ Of course, in most practical situations, one
simply wishes io findthe G or G corresponding to K(s) = 0, and the
fact that those G and G could also be obtained from other values of K ( s )
is not an issue.
The numerical superiority of our formulation of the optimal Hankel
model reduction results over that of Glover [5] is made transparent by
our example. The nonminimal (ug, ul0 = 0) and nearly nonminimal
