Stability analysis and artificial regulation design of genetic regulatory networks with multiple time-varying delays

We discussed the stability of genetic regulatory networks (GRNs) with multiple time-varying delays. Most of the results about the stability of them are based on the model in which the transcription and translation delays in every gene product take a same value. We generalized the model by a differential equation with multiple time-varying-delays to an extend field. We also considered the sufficient conditions for the GRNs' stochastic stability with stochastic noise. In the sense of linear matrix inequalities, delay-dependent stability criteria are obtained using Ito's formula and Lyapunov-Krasovskii functional. Then, the parameter fluctuations are considered elaborately, and a non-fragile gene feedback controller is developed, which is able to guarantee the exponential stability in mean square with stochastic noises. Finally, two examples are given, showing the proposed result with effectiveness.