where
F* (t) f(x,u,w) F (x = x (t) u u*()(2-41) w w (t)
and
G*(t) = af(x,u,w) tu x = x*(t)
u *(t) (2-42)
w =w t)
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) - ąt) (2-43)
, FF*(t) -G* (t) K1 -G* (t) K21
F AMt :=L -B (2-44)
f(x *(t)+x, u* (t)+u, w*(t)) - f(x*(t), u*(t), w*(t) fA(t, xA) AB (2-45)