An Intuitive Proof
q
Note that the system equation can be written as
q
State Feedback:
u=Fx
w
w
w
By Bounded Real Lemma: ||
T
zw
||
¥
<
g
Û
$
X =X*
³
0
such that
w
X(A+B
2
F)+ (A+B
2
F)*X+XB
1
B
1
*X /
g
2
+(C
1
+D
12
F)*(C
1
+D
12
F)=0
w
and
A+B
2
F+B
1
B
1
*X /
g
2
is stable
.