Robustness of interval gene networks with multiple time-varying delays and noise

In this paper, we investigate the problem how to establish the robust stability of uncertain gene networks with time-varying delays and noise. Specifically, we consider uncertain gene networks where the regulation occurs at the mRNAs level, and we obtain a sufficient condition for robust stability by Lyapunov method and inequality technique. Moreover, we show that these condition can be formulated as linear matrix inequalities (LMIs), which are easy to be verified by the convex optimization. Finally, two of the most common motifs are investigated to illustrate the effectiveness and the correctness of our results.