52
at atn mL(t-t )
eai'iix(t) ii < me 0 nxQlie
or
nx(t)n < m iixQlie
(mL-a)(t-t )
(4-15)
(4-16)
If L is sufficiently small so that
(mL-a) < 0
(4-17)
then we have the desired result.
Consider again the linearization of NCT given by (4-3). This can
be written as
xA(t) FxA(t) + FA^xA^^
(4-18)
The matrix F is defined as follows
F =
hA
F GK1 -GK2
-BH A
where
(4-19)
Fo = lf(x,.u>w)
3X
G0 = i.f(x,_u,wl
9U
x = 0
u = 0
w = 0
9
x = 0
u = 0
w = 0
(4-20)