Example 3.1:
Let us take
1( a + b + c (3-8)
(S-X1 (s1
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 hold true, tracking will occur for some initial state x0 and input
U(s). The input U(s) can be chosen as 1S w + 2 v + r (3-10)
(s-X T
where w, v, r Rm are vectors given by
v = {H[X1 I-T- G}- b
w = {H[X I-F]-1G}'I {a + HEX1I-F]'2Gv} (3-11)
r = {H[X2 I-]-IG}- 1c
The initial state x0 should be taken as
x -{ [F-xl]1 'Gw + [T-Xl11-2Gv + [F-X21] 1Gr } (3-12)
012