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Biochemical regulatory networks including genes, proteins and other regulatory molecules suffer from internal parametrical fluctuations (thermal, transcriptional, and splicing) as well as external noises (environmental and intercellular). Robustness is an essential property of intracellular biochemical regulatory networks to attenuate the effects of internal fluctuation and external noise. In this study, several system control schemes are proposed for the robust circuit control design of stochastic linear and nonlinear biochemical regulatory networks. First, the robust stability of genetic and proteomic regulatory networks is discussed under internal fluctuations. Then, the filtering ability of external noises is analyzed for stochastic biochemical regulatory networks. For the case where a biochemical regulatory network is not sufficiently robust to tolerate internal fluctuation and does not have enough filtering ability to filter the external noise, how to improve the robustness and noise filtering ability of stochastic biochemical regulatory networks by engineered control mechanisms is also proposed via biochemical circuit design. The proposed robust gene circuit design principles have potential applications for robust biosynthetic network design. Finally, two design examples are given in-silico to illustrate the design procedure and to confirm the performance of the proposed robust circuit design method.