Stabilization of genetic regulatory networks with mixed time-delays: an adaptive control approach

This paper addresses the stabilization problem for a class of genetic regulatory networks (GRNs) with mixed delays which include both the finite distributed time delay and the discrete time delay. The adaptive feedback control scheme is adopted to achieve the global asymptotic stability for the GRNs. By resorting to the integral partitioning technique and the delay fractioning approach, a novel Lyapunov-Krasovskii functional is constructed, and some sufficient criteria are established to ensure the closed-loop GRNs to be globally asymptotically stable. The conditions obtained are in the form of matrix inequalities and easy to be solved by resorting to the standard softwares in the Matlab. Finally, a numerical example is given to demonstrate the applicability and efficiency of the proposed approach.