Summary: 1948 IEEE TRANSACTIONS ON AUTOMATIC CONTROL, VOL. 39, NO. 9, SEPTEMBER 1994
Fig. 2. The structureof the fixed-lag smoother, 5 = 2.
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Fig. 3. Comparison between smoothers, 6 = 2: (a) H,-optimal (b)
Hz-optimal (c) suboptimalH,, y = 1.3~0(d) recursive fixed-point.
In this example we apply fixed-lag 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, nonminimum-phase 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 singular-value of the transference
from the disturbances w and U , to the estimation errors that was
generated by the optimal H, fixed-lag smoother of Section 111.
The disturbance transference of a standard Hz fixed-lag smoother
is brought for comparison. It is seen that the H, fixed-lag smoother
achieves a lower peak of disturbance transference. The decrease in
the latter peak is paid for by an inferior high frequency filtering.