
170 Synthetic Gene Network: Modeling, Analysis, and Robust Design Methods
For the simplicity of control design, suppose that the following
control input
e
uQ=
is employed to improve the robust synchronization
of the nonlinear stochastic coupled synthetic oscillation systems. In this
situation, the synchronization error dynamics in (8.13) should be modifi ed
as follows:
()
()
()
()
(,) ( ) (,) (,) ( ) (,)
em W emW
de F xs C Q I Gxs Hv dt F xs C Q I G xs dw=+⊗ ++ +⊗
(8.27)
where
()
()
()
NN
eeij
NN
CQ c Q R
×
×
=∈
is the coupling configuration
matrix, in which
()
()
()
1
1
eii s e
cQ N QQη
−
=− − +
if i = j, otherwise
() ( )
1
eij s e
cQ NQQη
−
=+
. Then, we can also obtain the ...