28
where
F*(t)
3f(x,u,w)
ax
*
x (t)
k
U (t)
*
W (t)
(2-41)
and
G*(t)
af(x,u,w)
au
x*(t)
u*(t)
w*(t)
(2-42)
'fc ^
Notice that the Jacobian matrices F (t) and G (t) are evaluated along
the trajectory which gives tracking of r*(t) with disturbance w*(t).
Often this trajectory is not known in advance, however, we shall defer a
more detailed discussion of this problem until a later chapter.
Let us make the following definitions:
xA(t)
x(t)'
'n(t)
(2-43)
FJ(t)
f^U, xA)
F*(t) -G*(t)Kx -G*(t)K2
-BH A
ff(x*(t)+x, u*(t)+u, w*(t)) f(x*(t), u*(t), w*(t))
(2-44)
(2-45)