 
Summary: 1948 IEEE TRANSACTIONS ON AUTOMATIC CONTROL, VOL. 39, NO. 9, SEPTEMBER 1994
Fig. 2. The structureof the fixedlag smoother, 5 = 2.
 l e t20
Fig. 3. Comparison between smoothers, 6 = 2: (a) H,optimal (b)
Hzoptimal (c) suboptimalH,, y = 1.3~0(d) recursive fixedpoint.
IV. EXAMPLE
In this example we apply fixedlag smoothing with 5 = 2, on a
simple system of the type of (2.la)(2.lc) where
Bk = [:.7094]. 1
Lk = [3  21 and CI,= [2 31.
This is a stable, nonminimumphase system. We assume that the
measurements have been continuing for a large period of time so that
(3.4a), (3.4b), (2.14a), and (2.14b) attain constant solutions. Fig. 3
depicts the Bode plot of the largest singularvalue of the transference
from the disturbances w and U , to the estimation errors that was
generated by the optimal H, fixedlag smoother of Section 111.
The disturbance transference of a standard Hz fixedlag smoother
is brought for comparison. It is seen that the H, fixedlag smoother
achieves a lower peak of disturbance transference. The decrease in
the latter peak is paid for by an inferior high frequency filtering.
