Robust hα control and uniformly bounded control for genetic regulatory network with stochastic disturbance

Robust H_∞ control and uniformly bounded control for a genetic regulatory network (GRN) with stochastic disturbance are considered, where the GRN is delayed with SUM regulatory functions. A sufficient condition is derived to ensure the mean-square stability of stochastic GRN. Robust H_∞ controller is then designed to stabilise the stochastic GRN in the mean square sense. Furthermore, some robust uniformly bounded controllers are also proposed to overcome the flaws where H_∞ control cannot be used. Finally, numerical results are given to verify the theoretical analysis in this paper.