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f(x) F = {x :
F (x) > 0}
f
r
(x) = rf(x) + φ(x) ,
r > 0
φ(x) =
log det F
−1
(x), x ∈ F
∞, x 6∈ F
.
n
x
n
f
r
(x) r = r
n
r
n
→ ∞
x
n
x
∗
F (x) < 0
t
F (x) − tI ≤ 0 t
min
≤ 0
t
min
< 0 t
min
> 0
,
t
,
x
c
c
T
x c
T
x <
,
x
λ λ ≤
Ψ + P
T
Θ
T
Q + Q
T
ΘP < 0 ,
Ψ, Q, P ,
Xc
0
Xmin
0
Ψ, Q, P,
0
Xmin
0
W
M
M
W
M
= (M) .
H
∞
˙x = Ax + Bu ,
x ∈ R
n
x
u ∈ R
n
u
u = Θx ,
Θ
x = 0
(A, B)
A
˙x = A
c
x , A
c
= A + BΘ
V (x) = x
T
Xx X =
X
T
> 0
˙
V = x
T
(A
T
c
X + XA
c
)x < 0 ∀x 6= 0 .
A
T
X + XA + Θ
T
B
T
X + XBΘ < 0 ,
X
−1
Y = X
−1
Y A
T
+ AY + Y Θ
T
B
T
+ BΘY < 0 , Y > 0 .
(Y, Θ)
Z = ΘY
Y A
T
+ AY + Z
T
B
T
+ BZ < 0 , Y > 0
Y Z (Y, Z)
Θ = ZY
−1
(A, B)
Y Z
Θ = ZY
−1
