Skewed Specifications
q
Suppose
P
D
Î
{P(I+w
D
):
D
Î
RH
¥
,
||
D
||
¥
<1
}
and
K
stabilizes
P
.
q
robust stability:
q
||
wT
i
||
¥
£
1
q
nominal performance:
q
||
W
e
S
o
||
¥
£
1.
•
robust performance is guaranteed
if
•
•
•
Condition number!!!!
Proof: Note that
T
ed
=W
e
S
o
(I+P
D
wKS
o
)
-1
=W
e
S
o
(I+P
D
P
-1
wT
o
)
-1