Asymptotic stability analysis of genetic regulatory networks with time-varying delay

This paper presents a analysis approach to asymptotic stability of the genetic regulatory networks with interval time-varying delays, the delays play an important role in dynamics of genetic networks and cannot be ignored in the modeling of genetic regulation due to slow biochemical reactions. The free weighting matrices are employed to deal with cross product items, and the convexity of the matrix function is fully utilized in our proof to obtain less conservativeness, by utilizing some techniques, both the upper and lower bounds of the delays are brought into final stability conditions. Based on the Lyapunov stability theory and linear matrix inequality, sufficient conditions are given to ensure the asymptotic stability of the genetic regulatory networks, the obtained conditions are derived in terms of LMIs which are easy to be verified via the LMI toolbox. Illustrative examples are provided to show the effectiveness of our proposed method.