Asymptotic stability of stochastic genetic networks with disturbance attenuation

Gene regulation is an intrinsically noise process, which is subject to intracellular and extracellular noise perturbations and environment fluctuations, moreover time delays play an important role in dynamics of genetic networks owing to slow biochemical reactions of transcription, translation and translocation. Basing on the above analysis, this paper presents a stochastic nonlinear model for genetic regulatory networks with SUM regulatory functions, sufficient conditions of the stochastic asymptotic stability with disturbance attenuation are derived in terms of LMIs, which are easy to be verified via the LMI toolbox. To show the effectiveness of the obtained results. Illustrative examples are also given at last.