具有区间时变时滞随机基因调控网络的弱保守性的稳定性判据

Less conservative stability criteria for genetic regulatory networks with interval time-varying delays and stochastic disturbances

研究一类带有随机干扰的时滞基因调控网络的稳定性分析问题。假定时滞是时变的,通过引入适当的Lyapunov泛函,分别利用自由权矩阵方法及Jensen不等式方法,建立基于线性矩阵不等式形式的稳定性判据,保证了所研究的基因调控网络是随机均方渐近稳定的。从理论和数值上对所提出稳定性判据与现有结果进行了保守性比较,说明了所提出方法的有效性。

Consider the problem of stability analysis of a class of delayed genetic regulatory networks （GRNs） with stochastic disturbances. The delays are assumed to vary in intervals. By introducing appropriate Lyapunov-Krasovskii functionals and employing free-weighting matrix approach and Jensen inequality approach, respectively, a pair of stability criteria in the form of linear matrix inequalities are established to guarantee the considered GRNs to be asymptotically stable in the mean square sense. Then, theoretical and numerical comparisons on conservativeness of the proposed stability criteria and one in literature are given, which illustrates the effectiveness of the proposed approach.