Proﬁle of the l
2
sensitivity measure, and proﬁle of
the parameters λ
1
and λ
4
during the ﬁrst 15 iterations
of the proposed algorithm are shown in Figs. 2 and 3,
respectively.
Iterations
J (P ,λ
1
,λ
4
)
Figure 2: l
2
Sensitivity Performance.
̂
̂
̂
̂
̂
̂
̂
Iterations
λ
1
λ
4
λ
1
λ
4
,
Figure 3: λ
1
and λ
4
Performances.
5 CONCLUSION
The problem of minimizing the l
2
sensitivity measure
subject to l
2
scaling constraints for 2D separable
denominator statespace digital ﬁlters has been for
mulated. An iterative method for minimizing l
2

sensitivity subject to l
2
scaling constraints has been
explored. This has been performed by using a La
grange function and an efﬁcient bisection method.
Computer simulation results have demonstrated the
validity and effectiveness of the proposed technique.
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MINIMIZATION OF l2SENSITIVITY FOR 2D SEPARABLEDENOMINATOR STATESPACE DIGITAL FILTERS
SUBJECT TO l2SCALING CONSTRAINTS USING A LAGRANGE FUNCTION AND A BISECTION METHOD
195