
in (6.20) and the optimal reference tracking in (6.21) for the synthetic gene
network are achieved simultaneously.
Based on the analysis above, the design steps of multiobjective H
2
/H
∞
reference tracking for the synthetic gene network are outlined as follows (Wu
et al. 2011b). (i) Based on the prescribed gene circuit topology as a guide, the
dynamic models of the synthetic gene network and reference model should
be constructed at fi rst. (ii) The desired standard deviations of parameter
fl uctuations M
k
in (6.18) to be tolerated by the stochastic gene network in
vivo are thus specifi ed. (iii) An adequate promoter set
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12
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n
ccc c= …
is
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