2.5. µSYNTHESIS AND D-KITERATION 63
frequency we would have,
D=
d1I1
...
dmIm
Ie
,
where the identity Ieis of dimensions dim(e)×dim(e).
The calculation of a new H∞controller requires a state-space realization of D(ω). For
each diin D(ω) we mustfit a tra nsfer function approximation, whichwe will denote by
ˆ
di(s). This is denoted by ˆ
D(s) in the above discussion. The observant reader will notice
that, as defined here, ˆ
D(s) is not of the correct input dimension to multiply P(s). We
must append another identity of dimension equal to the dimension of the signal y.The
final result is,
ˆ
D(s)=
ˆ
d
1
(s)I
1
.
.
.
ˆ
d
m
(s)I
m
I
e
I
y
and
ˆ
D−1(s)=
ˆ
d
−1
1(s)I
1
.
.
.
ˆ
d
−1
m(s)I
m
I
w
I
u
.
Throughout the theoretical discussion we have assumed that the perturbation blocks,
∆i, were square. The software handles the non-square case. This makes a difference to
ˆ
D(s)and ˆ
D
−1
(s). The identity blocks (Im, etc.) shownab ovewill be of different sizes
for ˆ
D(s)and ˆ
D
−1
(s) if the corresponding ∆iperturbation is non-square. Similarly,the
Iwand Iuidentities in ˆ
D−1(s) are not necessarily the same size as Ieand Iyin ˆ
D(s).