2.3.1
(2.76) - (2.83), , . . . X, . , .
, (2.98)
T [ n ´ n ].
.
"" (2.83):
(2.99)
, () (2.83) (2.99) [ n ´ n ] T. , A, B C
(2.100)
( . /3/).
2.3.2
(2.83) (2.85) (2.86) T , ..
, (2.101)
.
(2.100)
(2.102)
. 2.4.4.
2.3.3
(2.83) () T /20/:
,
M
.
2.3.4
n - . . 2.1.7.4. , , , .
|
|
, (2.103)
m < n.
. (2.104)
, . .
. . .
- . . , , (2.99). (2.104) n - . ( ) (. . 2.4.4). . . , , .. /20/.
. :
(2.87), (2.90)-(2.94), (2.96);
(2.99);
( 2.31-2.36).
. () . A, C A, B (2.104). , C B.
2.3.5
. ( 2.31) u 1(t), u 2(t), , um (t) U 1(s), U 2(s), , Um (s). m m ‑ U (s). X (s) Y (s).
W (s) F (s) ( ).
W (s) F (s) A, B C
|
|
,
s X (s) = AX (s) + BU (s)
[ s I - A ] X (s) = BU (s).
,
X (s) = [ s I - A ]-1 BU (s),
I [ m ´ n ] .
,
Y (s) = CX (s)
Y (s) = C [ s I - A ]-1 BU (s).
W (s) = [ s I - A ]-1 B; (2.105)
F (s) = C [ s I - A ]-1 B, (2.106)
.