We analyze the robustness of a system-level genetic circuit which is constructed by a bottom-up strategy. The latest trend in synthetic biology is to create large-scale and complex genetic circuits realizing desired programmable functions. An approach for the creation is bottom-up construction, that is, well-characterized small-scale circuits are coupled into large-scale system-level circuits involving desired programmable functions that can be predicted from the modules. However, in general, an intrinsic property in a circuit may be broken by internally connecting external circuits. We analyze a successful circuit created by a bottom-up construction strategy to identify the reason behind a successful synthesis. Utilizing the robustness analysis method based on the structured singular value, we can guarantee the validity of the bottom-up construction.