
104 Synthetic Gene Network: Modeling, Analysis, and Robust Design Methods
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
0
1,2 , ,
1
2
1
min
subject to 0
0
0
j
cLib
jm
n
TTTT
i i ik k k ik
k
d
n
TTTT
i i ik k k ik
k
PR
P
AcPPAc HQH BcMPMBc P
P
AcPPAc HQH BcMPMBc P
PI
r
Œ
=
=
=
>
È˘
++ +
Í˙
<
Í˙
Í˙
-
Î˚
È˘
++ +
Í˙
<
Í˙
Í˙
-
Î˚
Â
Â
…
(6.32)
where
0
{(0) (0)}
T
REXX=
denotes the covariance matrix of initial
condition
(0
X
, then the H
2
/H
∞
reference tracking in (6.24) and (6.25) can
be achieved.
Proof: See Appendix 6.3.
The LMIs-constrained optimization problem for multiobjective H
2
/H
∞
reference tracking design of the synthetic gene network in (6.32) could be
effi ciently solved by selecting an adequate promoter set from the redefi ...