Robust stability analysis of uncertain genetic regulatory networks with mixed time delays

This study is concerned with the robust stability problem of uncertain genetic regulatory networks (GRNs) with random discrete time delays and distributed time delays which exist both in translation process and feedback regulation process. By utilizing a novel Lyapunov-Krasovskii functional which contains some triple integral terms and takes into account the ranges of delays, we derive sufficient delay-dependent conditions to ensure the asymptotically stability of GRNs with mixed time delays. Moreover, based on the idea of delay decomposing'', reciprocally convex combination approach'', less conservative conditions are obtained by using the lower bound lemma together with Jensen inequality. In addition, two corollaries are also been presented. Finally, numerical examples are presented to show the effectiveness of our proposed methods.