1 2 1

H∞

4893

978-1-4244-1734-6/08/$25.00 c© 2008 IEEE

i

x

e

f

χvgt

χegr

i

x

Wc

x1 := pi, x2 := px, x3 := Wc, u1 := χegr

u2 := χvgt, d := mf

ρ1 = 0 Ne = 2500rpm ρ2 = 0χvgt = 84% ρ3 = 0

pi = 1400hpa1000rpm 4000rpm

0% 100%1000hpa 2000hpa

ρ1 = Ne/10000 ∈ [−0.15, 0.15]

ρ2 = χvgt/100 ∈ [−0.84, 0.16]

ρ3 = x1 ∈ [−400, 600]

px pi

4894 2008 Chinese Control and Decision Conference (CCDC 2008)

⎛⎝ x1

x2

x3

⎞⎠ =

⎛⎝ −12.6 + 0.05ρ3 8.2 + 0.001ρ3 0

1.01 + 4.0ρ1 −2.08 00.12 + 4.04ρ1 −0.37 − 0.44ρ2 −1.33

⎞⎠

⎛⎝ x1

x2

x3

⎞⎠ +

⎛⎝ 0

2.060

⎞⎠ d

+

⎛⎝ 0 0

−25.65 40.32−18.27 0

⎞⎠(

u1

u2

)

y =

(0 0 11 0 0

)⎛⎝ x1

x2

x3

⎞⎠

x = A(ρ)x + B1(ρ)ω + B2(ρ)u

z = C1(ρ)x + D11(ρ)ω + D12(ρ)u

y = C2(ρ)x + D21(ρ)ω

A ∈ �n×n, D12 ∈ �p1×m2 , andD21 ∈ �p2×m1

A(ρ), B1(ρ), ...D21(ρ)ρ

ρ(t) :=(ρ1(t) ρ2(t) · · · ρN(t)

)ρ(t)

H Hd

ρi(t) =(

ρi, ρi

), ∀t � 0

ρi(t) =(

νi, νi

), ∀t � 0

L2

xK = AK(ρ, ρ)xK + BK(ρ, ρ)y

u = CK(ρ, ρ)xK + DK(ρ, ρ)

L2

γ ω z

∫ t

0

zT zdτ � γ2

∫ t

0

ωT ωdτ, ∀t � 0

ρ(t)

ρ

(BT

2(ρ) DT

12(ρ)

)and

(C2(ρ) D21(ρ)

)H

ρ ρ

L2

γ

V (x, xK , ρ) :=

(x

xK

)T

P (ρ)

(x

xK

)

P (ρ)(13)− (14)

X(ρ) Y (ρ)(16), (17), (18)

(ρ, ρ) H × Hd

NX NY(BT

2(ρ) DT

12(ρ)

) (C2(ρ) D21(ρ)

)

X(ρ) Y (ρ) γ

2008 Chinese Control and Decision Conference (CCDC 2008) 4895

(NX 00 I

)T

⎛⎝ X + AX + XAT XCT B1

C1X −γI D11

BT1

DT11

−γI

⎞⎠(

NX 00 I

)≺ 0

(NY 00 I

)T

⎛⎝ −Y + AY + Y AT Y B1 CT

1

BT1

Y −γI DT11

C1 D11 −γI

⎞⎠ (

NY 00 I

)≺ 0

(X II Y

)� 0

H∞

We1 = We2 =2

s + 0.01Wu1 = Wu2 = 1

Wb1 = Wb2 =0.1s

0.01s + 1

Wn1 = Wn2 =0.1(s + 1)

0.1s + 1

X YX0 Y0

X, Y

X0, Y0 X0, Y X, Y0 X, Y

γ 0.87 0.84 0.72 0.66

γ = 0.87

X Y

X = X0 + ρ1X1 + ρ2X2 + ρ3X3

Y = Y0 + ρ1Y1 + ρ2Y2 + ρ3Y3

X Y

X Y0

X Y0

ρ3

mf

mf

4896 2008 Chinese Control and Decision Conference (CCDC 2008)

Ne

mf

Ne

mf

Ne

Ne

Ne

2008 Chinese Control and Decision Conference (CCDC 2008) 4897

5

l2

h∞

4898 2008 Chinese Control and Decision Conference (CCDC 2008)