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˙x = Ax + Bu
y = Cx
u = Ly .
k k 6= 0
max
i
λ
i
(A + BLC) < γ/2 ,
K F
K F Y = Y
T
> 0
(A + BK)Y + Y (A + BK)
T
< γY
(A + F C)Y + Y (A + F C)
T
< γY .
L
A+BLC
z < γ/2
f(z) = z + ¯z − γ
Y = Y
T
> 0
(A + BLC)Y + Y (A + BLC)
T
< γY .
K = LC
F = BL
L
Y = Y
T
> 0
(AY + Y A
T
− γY ) + Y C
T
L
T
B
T
+ BLCY < 0 .
Ψ + P
T
Θ
T
Q + Q
T
ΘP < 0 ,
Θ = L
Y = Y
T
> 0
W
T
B
T
(AY + Y A
T
− γY )W
B
T
< 0 ,
W
T
CY
(AY + Y A
T
− γY )W
CY
< 0 .
(AY + Y A
T
− γY ) + Y K
T
B
T
+ BKY < 0 ,
Θ = K
Y = Y
T
> 0 K
W
T
B
T
(AY + Y A
T
− γY )W
B
T
< 0 ,
F Y
(AY + Y A
T
− γY ) + Y C
T
F
T
+ F CY < 0 ,
W
T
CY
(AY + Y A
T
− γY )W
CY
< 0 ,
γ
K F Y = Y
T
> 0
γ
∗
L
γ
∗
< γ < 0 Y > 0
K F
L
γ
K F Y = Y
T
> 0
K F
γ
F
K
W
T
B
T
(AY + Y A
T
− γY )W
B
T
< 0 .
γ
Y > 0 γ
Y
γ K
K F
X(A + BK) + (A + BK)
T
X < γX
X(A + F C) + (A + F C)
T
X < γX .
X = Y
−1
k = 0
X = X
T
> 0 Y = Y
T
> 0
W
T
C
(XA + A
T
X)W
C
< 0 ,
W
T
B
T
(AY + Y A
T
)W
B
T
< 0 ,
X I
I Y
≥ 0
X I
I Y
= n
x
,
n
x
(X, Y )
(X + Y )
K
0
γ
Y
K
0
j = 0
K = K
j−1
γ = ˆγ
j
X(A + BK) + (A + BK)
T
X < γX
W
T
C
(XA + A
T
X − γX)W
C
< 0 ,
F
j
= −µX
−1
C
T
µ > 0
µ
F = F
j
γ = γ
j
W
T
B
T
(AY + Y A
T
− γY )W
B
T
< 0
(A + F C)Y + Y (A + F C)
T
< γY ,
K
j
= −µB
T
Y
−1
µ > 0
|(γ
j
−γ
j−1
)/γ
j
| < ε
j = j + 1
max{ˆγ
j
, γ
j
} < 0
γ = −2
Θ = −3.2083
ˆγ = 0.5095·10
−5
γ = 0.5428·10
−5
γ < 0
H
∞
H
∞
