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. 6
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tk tk+1 ]: -
, tk = 0 -
0 T0 ]:
tjr (j = 1 2 : : : N r = 1 2 : : : dj ),
j- .
tjr = tj0 + rTj tj0 Tj
{" .
"
, k
Tj . -
S
, - -
y(t) = S(x(t0 ) u t0 t] ) . ,
-
. -
kT0 ,
u(tk ) u(t) -
tk tk+1] ( . 6.4.2. 6.7.). -
tk
156
x k + 1] = Px k] + Qu k] y k] = Cx k] + Du k] k = 0 1 : : : (6.49)
:
PQCD
. , -
(6.49) (6.8)
k;1
X
k ; j ; 1]Bu j]
x k] = k]x0 + k = 1 2 3 ::: (6.50)
j=0
k]
0] = I
k + 1] = P k] k = 0 1 2 ::: : (6.51)
(6.51) , P = 1]: u k] 0
xi 0] = ei = 0 : : : |{z} : : : 0]T :
(6.50), xi 1] = 1]xi 0] 1
i
, xi 1] i- 1] , -
, P: -
i = 1 2 ::: n P:
, P n -
0 T0 ] -
. Q
x 0] = 0 ui k] ei i = 1 2 : : : m : ,
B = x1 1]...x2 1]... : : : ...xm 1]]: xi 1] -
i = 1 2 ::: m : -
...y ... : : : ...y ]
C C = y1 2 n
u = 0 xi = ei i = 1 2 : : : m k = 0:
yi {
D
x = 0 ui = ei i = 1 2 : : : m k = 0: , -
CD
. -
-
. .
. - -
- -
:
x1 k1 + 1] = K1 T1u1 (k1 T1 ) + x1 k1 ]
157
x2(t) = u(t)
_
u1 k1 ] = g(k1T1 ) ; y(k1 T1 ) (6.52)
u(t) = x1(k1 T1 ) ; u2 k2 ]
u2 k2 ] = K2 y(k2 T2)
y(t) = x2(t)
kj = E(t=Tj ) j = 1 2 g(t) { ( )
{ T1 T2 { -
T1 = 2T2 K1 K2 { T y(t) { -
x = x1 x2] { -
. (6.52) (6.49),
.
T
g(t) 0 x(0) = 1 0] : (6.52) t = TT1 ( -
x(T1 ) = 1 T2 (2 ; K2 T2 )] :
, T1 = 2T2 ) T
, x(T1 ) = ;2K1 T2 (1;K2 T2)2 ]T :
x(0) = 0 1]
,
P = T (2 ; K T ) (1;2K1 T2 )2 :
1
; K2T2
2 22

Q x(0) = 0 g(t) 1:
Q = 2K1 T2 0]T :
(6.52), CD
(6.52)
C = 0 1] D = 0:
(6.49) (6.52)
t = 0 T1 2T1 : : : :
-
.
n + m: 0 T] T
{ .
.
-
( -
) .
-
.
(6.13), -
. -
-
.
158
6.10. . -

-
: -
, -
-
. ,
.
.

-
.
6.10.1.
. , -
, -
( ) A
(6.13) : Resi < 0
det(si In ; A) = 0 i = 1 : : : n ( 3, 15, 76, 79, 66]).
, (6.14) -
det(zi In ; P) =
: jzi j < 1
,
0 i = 1 : : : n: -
, ,
. 53]
. fsig
f(s)
n n- A zi n n-
zi = f(si) i = 1 : : : n: 2
P =f(A)
(6.17), P = eAT0 : -
zi P
zi = esi T0 i = 1 : : : n : , T0 > 0 -
Resi < 0 () jzi j < 1
(6.13), (6.14) .
. 6.5.2. .
2. . , (6.20) -
P = In +AT0: , zi = 1 + siT0, i = 1 : : : n :
jzij < 1 -


159
( i +1)2 + i2 < 1 i = T0 Resi i = T0 Imsi i = 1 : : : n : (6.53)
(6.53) , -
,
,
(;1 |0):
T0 < 2 min jResi j : (6.54)
i js2 j i
, -
, , -
T0 =2 > T. -
(s1 2 = | ) T0 > 0: 13

-
, (
) T0:
3. . (6.23),
, zi = 1 ;1s T , i = 1 : : : n :
P = (In ; A );1:
i0
jzi j < 1
,

( i ;1)2 + i2 > 1 i = T0 Resi = T0 Imsi i = 1 : : : n : (6.55)
i
(6.55) , -
, , -
(1 |0): -
, -
-
( ) T0 > 0:
, -
: -
-
. , -
( ,
T0 ! 0 zi
,
13
zi = esi T0 :
,

160
O(T0 ) ): -
" " .
4. =. -
, () =
() jzij < 1 :
T0 > 0 Resi < 0 -
, (6.13)
(6.14). ,
-
(6.24) ( ) (6.25). ,
O(T03 ) O(T05) , -
,
-
.
. 6.1 -
sT0. , -
( 6= 0) -
.




. 6.1.
.

6.10.2.
-

161
, , -
{ 3, 72]. ,
.
x(t) = f(x t)
_ x(0) = x0 t 0: (6.56)
-
xk+1 = '(xk k)
k= 0 1 2 : : : { xk -
( ),
x(t) -
tk = kh h>0 { . 14
'(xk k) f(x t) -
.-
, , -

xk+1 = xk + f(xk tk )h tk = k h k = 0 1 2 ::: : (6.57)
, f(x t) x
(6.56)
x(t) = Ax + (t)
_ (6.58)
A { n n- . (6.57) -

xk+1 = (In + Ah)xk + (tk )h: (6.59)
, (6.59)
(6.14), PQ -
(6.20) .
-
. 6.10.1. -
: A T0 = h -
(6.53). , -
15

(
14
.
-
15
(6.56),
@f(x t) :
A @x
162
), , -
h . -
.
, , h
, -
.
-
,
(6.19). -
, -
. -
" ",
3, 72].
, -
h , -
- . 16

. , (6.56) -
x(tk+1) x(tk ). ,
" " (6.56)
x( ) = ;f(x tk+1 ; ) x(0) = x(tk+1)
_ 0:
(6.57)
xk = xk+1 + f(xk+1 tk+1)h: (6.60)
xk+1 -
xk+1 = '(xk k): (6.58),

xk+1 = (In ; Ah);1 (xk + (tk+1)h) (6.61)

(0 1). (6.61) -
(6.58) h > 0. 17

-
16
, -
.
17
6.10.1. (6.55).

163
, -
. , -
(6.60).
-
,
. -
(6.58), (6.60)
. , -
PQ (6.58) -
(6.14) , -
(6.14) -
xk : -
-
. -
, , 13, 72],
. 11.4.5. ( . 277),
.
6.11. {
-
-
(" ") , -
{ (6.14) -
( ) (6.13).
,
.
, , -
-
(6.15). 18

P =1 AB -
A = 0 B = Q=T0:
CONTROL
18
SYSTEMS MATLAB 139].

164
P = 0P I Q
mn m
(n + m) (n + m)
A = (log P )=T0 : n n- A n m- B
(6.13) , -
A

A= A B :
,
.
6.12.
1. -
e J -
Jt
( . . 139).
eAt
2.
1 . 126 .( {
, . 6.5.1.).
3. .2 -
( . . 142).
4.
( . 6.5.1.)
( . . 6.4.2. 6.6.)
15, 76]
.
15, 76] , z-
.
5. . 6.4.2. -
.
6. -
u(t) 6 0 (
x0 t<0
u(t) t). . 6.3. .
133, .
7. . 6.3.
, Q{ .
165
7. {

7.1.
. -
-
,
{ -
. -
-
.
3, 30, 44, 47, 83].
1. x
x0 ( - ) -
u t0 t1 ] t0 t1 ]
0 < t1 ; t0 < 1 , -
u t0 t1 ] x(t0 ) = x0
x(t1 ) = x :
2. ( -
),
. ,
, -
.
.
,
, , -
, -
: u1 (t) = sat(u(t)) T x(t) + x(t) = u1 (t) (u
_
{ , sat( ) { . 7.1). -
, u(t) , -
fx0 : jx0 j < 1g
fx0 : jx0j > 1g: 2
. 1.1. -
, -
x(t0 ) = x0 y(t1 )
u(t) t0 t1 ]:
x0 - :

166
. 7.1. .
, -
,
.
3. x00 x00 -
0
, x0 x00, u(t) -
0 0
0 x(t0 ) = x00
x(t0 ) = x0 0
( . 7.2).




, x00 x00.
. 7.2. 0

4. ,
, ..
. -
,
{ {
, { .
5( ).
( ) ( ), -
0<T <1
, x t0 -
u t0 t1 ] t1 = t0 + T ,
x(t0 ) = 0 u t0 t1 ] x(t1 ) = x :
1. ,
, .. -
.

167
2.
, x
T > 0:
-
-
,
. 93]
,
-
-
,
..
6( ). -
( ) , -
0<T <1 , t0 x(t0 ) u t0 t1 ] (t1 = t0 +T)
y t0 t1 ] u t0 t1 ] x(t0 ):
3.
x(t0 ) T > 0:
4. ,
, , ,
, y t0 t1 ]
x(t0 ) u(t) 0: :
, y(t) = 0 u(t) = 0
t 2 t0 t1 ] : x(t0 ) = 0:
,
t0 ( , t0 = 0): 1
-
( ). , -
, -
.
.
, -
-
. -
1
47],
.
,
.

168
. -
-
.
7. ,
.
-
: -
, -
. , -
(
).
,
.
8. ,
.
, -
.
9.
.
7.2.
.
-
3, 30, 83].
1. ( ).
Q = B AB : : : An;1 B (n nm) (7.1)
, 2 rankQ = n n{ -
. 47], -
Q: , n
,
2
- ( ) . -
3, 53, 66, 115].

169
, -
. SIMO-
( , u(t)2R) Q -
n
Q : det Q 6= 0:
2. T
det T 6= 0 , ,
˜ = TAT ;1 B = TB
˜ ˜˜
A AB
A = 0A11 A12 B = 0 B1 :
˜ ˜ (7.2)
A22
n2 n1 n2 m
˜˜
AB , -
x2R n
˜
x = colf˜1 x2 g x1 2 R ˜2 n1 x 2 Rn2 n = n + n
˜ x˜ ˜ -
1 2
x2
˜ -
, ( x1 )
˜ . ,
x2 :
˜ -
colf0 x2 g
˜ -
.
(.. A22
{ ), (
3

)
˜˜
AB
47, 174]. -
. 7.3, ).
3. B -
A , , n. 4

- B -
X A dimX A < n v -
XA
x(t) = Ax(t) + Bu(t)
_
x0 2 X A:
, -
,
, , -
3
.
4
m>1
.
A , ,
n B:
.
3.1.2. . 83

170
. 7.3. () -
( ).

.
D(s) = sn + d1 sn;1 + : : : + dn
4.
di 2R { , m n-
det(sIn ; A + BK) = D(s):
K
,
-
{ -
-
u(t) = ;Kx(t). 5

5.
W(s) = C(sI ; A);1B
C ,
( s) .
CeAt B
6. =0 t t1 < t < t2
C 2Rn C = 0:
( . . 6.2. . 133)
-
C = 0:
T
BT z = 0
7. A z = 0z
2 C z 2Rn z = 0 30, 83].
0
, , :
8. (A B) , m n-
K (A + BK B) .
5
9.

171
, -
u(t) = Kx(t) K
.
9. (A B) si { -
siIn ; A
A, d
B 30]. 6

, m=1( m > 1 rankB = 1)
d=1 ..
(A B) , si -
A:
10. t1 > t0
Zt1 T
W(t0 t1) = eA BBT eA d (7.3)
t0
, -
.
,
30], W(t0 t1 )=W(t0 t1 ) > 0 T
t1 >t0 : -
, u t0 t1] x(t0 ) = x0
T
u(t) = B T eA (t1 ;t) C
x(t1 ) = x1
C{ n- .
(6.9, . 130)
R t1 A(t1 ; ) T AT (t0 ; )
x2 ; eA(t1 ;t0) = t0 e BB e x2 ; eA = W( )
d
Z T
eA BBT eA d :
= t1 ; t0 > 0 W( ) = W(0 ) =
0

W( ) > 0 , det W( ) 6= 0
;
);1 x1 ; eA
C = W( x0 : ,
;
T AT (t1 ;t)
e W( );1 x1 ; eA x0 :
u(t) = B (7.4)
-

-
6
siIn ; A
. -
A si.

172
x(t0 ) = x0 x(t1 ) = x1 -
= t1 ; t0
t1 > t0 , (A B) .
, -
W(t0 t1) -
. ,
3, 30, 83].
-
.
( )
x(t) = A(t)x(t)+B(t)u(t)
_ , -
t1 (t0 < t1 < 1)
, t0
Z t1
(t1 )B( )B T ( ) T (t1 )d
W(t0 t1) =
t0
( (t ) { ,
. . 6.3).
(u(t) 2 R m = 1)
SIMO- -
.
˜˜
11. (A B) ,
˜
det(sIn ; A) det(sIn ; A) -
˜
T det T 6= 0 A=TAT ;1
,
˜
B = TB:
˜ ˜
T = Q Q;1 Q Q;1
T
˜˜
{ (A B) (A B) -
. , -
SIMO- (m = 1) -
( . . 3.2.2.),
˜{
A -
( )
2 3
0 1 0 ::: 0
60 1 ::: 0 7
0
6 .. 7
˜6
A=6 . 7
7
40 0 ::: 1 5
0
;an ;an;1 ;an;2 : : : ;a1
˜
det(sIn ; A) = sn + a1 sn;1 + + an

173
˜
B = 0 0 : : : 0 1]T . 7
n 1-
12. (1 n)- C -

B(s)
W(s) = C(sI ; A);1 B = det(sI ; A) (7.5)
{ (..
W(s) n).
n;
13. B(s)
1 (1 n)- C
(7.5).
12 -
: W(s) -
, . -
.
7.3. .
-
. ,
CeAt x0 = 0
.6
t t1 t2 t1 < t < t2 x0 = 0: -
, y(t) = Cx(t)
, ,
.
-
rankQ = n n{ -
, Q = CT
,Q {
TT T n;1 T
A C : : : (A ) C ] n nl: , MISO-
(l = 1) -
.
, -
,
(A B) -
T T
(A B ), , , -
(A C)
˜˜
(A B) -
7
.
.1.


174
(AT C T ): -
,
AT B
A
CT :
, , , -
-

A = A11 0n1 n2 C = C1 ...0l
˜ ˜ n = n1 + n2 :
n2
A21 A22
, -
,
, ( )
.
-
˜ ˜
A C
47, 174]. -
. 7.3, ).
, MISO- (y(t)2
R) n 1- B ,
W(s) = C(sI ; A);1 B { -
, n: , -
, m=l=
1 -
SISO- .
MIMO-
-
30].
A -
W(s)
M(s)
lim A(s)M(s) 6= 0 (7.6)
s!si
A(s) = det(sIn ; A) { -
A: SIMO MISO- -
W(s) -
( ) -
, n:
SISO- .
MIMO- -
,
30].
175
(A B)
, si A(s) =
W(s)
det(sIn ; A) M(s)
(si In ;A)
, d
(7.6).
. rB = rank(B) rC = rank(C):
, si -
d > rB (A B) , d > rC
(A C) . -
W(s) d rB
d rC : , (7.6)
M(s)
d: d , (7.6) -
,
maxfrB rC pi g pi { si 30].
-
T
- Q ..
T
x Q x = 0:
,
x = 0:
-
A bi bi
i = 1 ::: m { B:
-
n;1 B] 88].
L = CB CAB : : : CA
-
. -
. 1.4.3. . 31
.
. 94 . 3.2.4.
Q (1.18) , , -
. -
-
. . 433 3
obsvf MATLAB 139].
,
Abar, Bbar, Cbar, T, K] = obsvf(A, B, C)
-
. (A C)

176
r n, T
Abar = TAT ;1 Bbar = TB Cbar = CT ;1
, -
8


Abar = Ano A12 Bbar = Bno Cbar = 0 Co ]
0 Ao Bo
Co(sI ; Ao);1 Bo C(sI ;
(Ao Co) {
;1B:
A)
-

A= 0, 1, 0, 0 0,-k/M,0,0 0,0,0,1 -g/L 1,0,g/L 1,0]
B= 0 1/M 0 0] C= -1 0 1 0]/L 1
{ (1.18)
n,d]=ss2tf(A,B,C,D,0)
{
Abar,Bbar,Cbar,T,K] = obsvf(A,B,C)
{
Co=Cbar(1,2:4), Bo=Bbar(2:4,1), Ao=Abar(2:4,2:4)
{
no,do]=ss2tf(Ao,Bo,Co,0,1)
Qo=obsv(Ao,Co) do=det(Qo)
{ (Ao Co)
.

2 3 2 3
01 0 0 0
˜ = 6 0 ;0:5 0:5 11:6 7 ˜ = 6 0:71 7
A 6 0 0:5 ;0:5 11:6 7 B 6 ;0:71 7
4 5 4 5
00 1 0 0
˜
C = 0 0 0 1:68] K = 1 1 1 0]:
2 3
0:71 0 0:71 0
6 7
T = 6 0 ;0:71 0 0:71 7 :
0:71
40 0 0:71 5
;0:71 0 0:71 0
T -
8 obsvf
T ;1 = T T .
53, 115], , obsvf
, ,
˜˜
A C:
. 175

177
( -
s) ,
(3.15),
. 93.
2 3
0 0
1:68
det Qo = ;2:34:
Qo = 4 0 05
1:68
0:84 ;0:84 91:6
7.4.
1. , -
.
2. , A11 A22
(7.2) ( . 170)
T 47].
3. , -
(7.2), ,
( . 81),
, .. A11 (7.2)
47].
4. -
:
_
X(t) = AX(t) + X(t)B + CU(t)D
X(t) { n n- U(t) { r m-
( ) A B C { n n D { m n- 3].
5. (A B) 3]
2 3 23
0101 1
6 7 607
A = 61 0 1 07 B = 617:
40 1 0 15 45
1010 0
(7.3) W(0 1)
6.
x(t) + x(t) = u(t):
7. -
, 174]. ,

x k]2Rn u k]2R
x k + 1] = Ax k] + Bu k] k = 0 1 2 : : : (:7.7)

178
, -
, n .
.
) Q{ (7.7). -
riT i- Q;1
2 rT 3
1
T
;1 = 6 r.2 7 :
67
Q 4 .. 5
T
rn
u k] = ;rn;k An x 0] k = 0 1 2 : : : n;
T
,
1 (7.7) -
.
T
K = rn An :
) ,
u = ;Kx ,
. 7. .
)
x k + 1] = (A ; BK)x k]:
A ; BK .
?
8. (7.7) 174]
A= 2 1 B1 = 0 B2 = 1 :
02 1 0
) B1 B2 .
) -
, -
x 0] = 2 :
1
9. si A
x(t) = Ax(t)+Bu(t) u(t)2R
_ 174]. -
, ,
, , A
, B( ) -
.
.
10. , -
, , (7.7) -
, -
x k + 1] = (A ; BK)x k] + Bu k] 174]. ( : ,
179
, -
.)
11..
174]
w(t) = A11 A12 = w(t)
_
y(t)
_ A21 A22 y(t)
y(t) { . ,
(A11 A21 ) .( :
-
, . . 174).
12. 174]
x1(t) = x2 (t) + u(t)
_ x3(t) = x3(t) + w(t)
_
x2(t) = ;2x1 (t) ; 3x2 (t)
S1 : S2 :
_ z(t) = x3(t)
y(t) = x1 (t) + x2 (t)
{ .
) , , -
S1 S1 :
) (w(t) = y(t))
S3: , -
.
)
S4 ( . . 7.4).
.




. 7.4. 12 ).




180
8. -

8.1.
. -
, , -
.
-
-
{ -
. , -
-
. -
-
,
.
, -
,
.
. ( -
) , -
.
( ) -
3, 8, 47, 76, 88, 93].
:
{ -
, ..
t
t;T T > 0
{ -
{ -
, .. t
, t + T T > 0:
, -
. -

181
, -
- . -
. 1


" ". -
,
. -
-
.
:
x(t) = A(t)x(t) + B(t)u(t) + f(t)
_
y(t) = C(t)x(t) + v(t) x(t0 ) = x0 t t0: (8.1)
x(t)2Rn { u(t)2Rm y(t)2Rl
- A(t) B(t) C(t) { -
.
f(t) " " v(t): ,
( )
u(t) y(t)
x(t) f(t) v(t) { . -
x(t).
^ x(t)
^ -
, -
( , ) -
x(t) (^ (t) ! x(t) t ! 1)
x
x0:
, -
-
. -
2


.
.
, , -
1
-
. -
. 12.3. ( . 307)
.
, 64], 8, 23, 76, 93, 103, 106, 191].
, -
2
,
. -
, -
.

182
. (8.1)
.
, (8.1)

x k + 1] = A k]x k] + B k]u k] + f k]
y k] = C k]x k] + v k] x t0 ] = x0 k = k0 k0 + 1 : : : (8.2)
-
x k]:
^
8.2.
( , -
)
,
,
,
, , (
).
( . 8.1).




. 8.1. -
.
-
( ).
, -
-

183
. -

_
x(t) = A(t)^(t) + B(t)u(t) + L(t)(y(t) ; y (t))
^ x ^
y (t) = C(t)^ (t) x(t0 ) = x0 t t0:
^ x ^ ^ (8.3)
x(t) 2 Rn {
^ ,
y (t) 2 Rl{
^ L(t)
{ n l- -
.
L(t):
, ,
, (
,
). :
(. " -
"), (
, . . 12.6.5.).
-
"(t) = (x(t) ; x(t)):
^ (8.1)
(8.3),
"(t) = (A(t) ; L(t)C(t)) "(t) + f(t) ; L(t)v(t)
_
"(t0 ) = "0 = x0 ; x0 t t0:
^ (8.4)
, "(t) -
"0 = x0 ; x0^
f(t) v(t): -
A (t) = A(t) ; L(t)C(t):
"(t)
"(t)
, ABCL .3
-
det(sIn ;A ) . . A = A;LC:
, -
f(t) v(t) ,
"(t) ! 0 t!1
x0 x0 :
^ A -
( A C (8.1)) L
3
. ,
, 3, 47].

184
.
. 7.3. , -
L -
A . -
, L
. 4

(L = 0) -
. ,
- -
. A -
L,
. (8.4), -
f(t)
, v(t) { .
L
-
.
L
, , -
. -
Wf" (s) Wv" (s)

Wf" (s) = (sIn ; A + LC);1 Wv" (s) = ;(sIn ; A + LC);1 L:
jj"(t)jj)
(
L -
47].
-
L .


det(sIn ; A ) det(sIn ; A + LC) = sn + 1sn;1 + + n :(8.5)
-
i
L: , -
n
"(t) -
, , ,
4
.
.

185
nl L: -
AC ( l=1 ). -
i
(l > 1)
L . ,
L
-
.
-
( ., , 3]). -
(8.5)
,
, : 47, 76]
n
Ys
; e|( 2 + 2 2n )
;1
det(sIn ; A ) = !0
=1

!0 {
.
(8.2)
:
x k + 1] = A k]^ k] + B k]u k] + L k](y k] ; y k])
^ x ^
y k] = C k]^ k] x(t0 ) = x0 t t0 :
^ x ^ ^ (8.6)
-
det(zIn ; A ) det(zIn ; A + LC)
zi
. -
. , (8.6) L -
zi = 0 i = 1 2 : : : n
, -
nT0 n{ , T0 { -
. 5

, ,
, -
.
n
, ,
5
, -
T0 .

186
, -
(. 8 . 7.1.)
,
-
(8.5).
8.3.
-
, ,
n: , -
. -
n;p p = rank C
( p = l:) -
,
3, 174].
-
,
x(t) = Ax(t) + Bu(t) y(t) = Cx(t):
_ (8.7)
p n- C p:
-
(8.7). (n;p) n-
V ,
T= V
C
. ,
rank C = p: x(t) = Tx(t)

x(t) = w(t) gn ; p
y(t) gp
w(t) 2 Rn;p y(t) 2 Rp . .
p
. T,

w(t) = A11 A12
_ w(t) + B1 u(t): (8.8)
y(t)
_ A21 A22 y(t) B2
187
n;
p ( ) u(t) y(t):
,
.
(8.8) -
(n ; p) p- E
.
w(t);E y(t) = (A11 ;EA21 )w(t)+(A12 ;EA22 )y(t)+(B1 +EB2 )u(t):
_ _

;
w(t) ; E y(t) = (A11 ; EA21 ) w(t) ; Ey(t) +
_ _
+(A11 E ; EA21 E+ A12 ; EA22)y(t) + (B1 ; EB2 )u(t):
v(t) = w(t) ; Ey(t)
v(t) = (A11 ; EA21)v(t)+ (8.9)
+(A11 E ; EA21E+ A12 ; EA22 )y(t) + (B1 ; EB2 )u(t):
v(t) { ,
u(t) y(t) . , -
v(t)
v(t) = (A11 ; EA21)^(t)+
^ v
+(A11 E ; EA21E+ A12 ; EA22 )y(t) + (B1 ; EB2 )u(t): (8.10)
, (8.9) (8.10),
v (t) ; v(t) :
^
; ;
_
v (t) ; v(t) = A11 ; EA21 v(t) ; v(t) :
^ _ ^
v (t) ; v(t) ! 0,
, ^ -
A11 ; EA21 :
v(t)
(8.8), -
. w(t), y (t)
^^ x(t)
w(t) = v (t) + Ey(t)
^ ^ y (t) = y(t):
^
T ;1
x(t)
^ (8.7).
188
A11 ; EA21 :

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