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5 CONCLUSIONS
This paper has developed a simplified method of com-
puting an improved l
2
-sensitivity measure for state-
space digital filters by reducing the number of the
Lyapunov equations. The simplified method has also
been expanded into a class of 2-D state-space digital
filters. First, a conventional improved l
2
-sensitivity
for state-space digital filters has been reviewed and
its computation method has been simplified with two
novel forms such that the number of the Lyapunov
equations is reduced. Next, the resulting method has
been applied to a class of 2-D state-space digital fil-
ters. This has been done more precisely by taking into
account 0 and ±1 elements in the filter. Finally, two
numerical examples have been presented to explain
the validity and effectiveness of simplified methods
of computing more precise (improved) l
2
-sensitivity
measures for 1-D as well as a class of 2-D state-space
digital filters.
The simplified method has also been investigated
for computing a more precise l
2
-sensitivity measure in
2-D state-space digital filters described by the Roes-
sor model (Roessor, 1975) and the results will appear
elsewhere.
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