42
Example 3.1:
Let us take
R*(s)
is-V
a +
(S-X1)
b +
(s-L)
(3-8)
where a, b, c e RP are constant vectors. Also, for simplicity of this
example let
W*(s) = 0
(3-9)
We now show that when conditions (1), (2), and (3) used in Theorem 3.2
ie
hold true, tracking will occur for some initial state xQ and input
U(s). The input U(s) can be chosen as
u(s) = w + ,
(s V (s-xj)
Vv +XCTr
where w, v, r e Rm are vectors given by
v = {H[x1I-F]1G}"1b
w = {H[X1I-F]_1G}"1 {a + H[x1I-F]"2Gv}
r = {H[x2I-F]'1G}'1c
The initial state
should be taken as
(3-10)
(3-11)
x* = -{ [F-x1I]"1Gw + [F-x1I]"2Gv + [F-X2I]1Gr }
(3-12)