Improved stochastic integral inequalities to stability analysis of stochastic genetic regulatory networks with mixed time‐varying delays

Abstract

This study investigates the problem of mean-square asymptotic stability analysis of stochastic genetic regulatory networks with mixed time-varying delays. The innovation of this study lies in that several stochastic integral inequalities are improved based on auxiliary function integral inequalities. Thereby, less conservative mean-square asymptotic stability criteria are derived by constructing Lyapunov–Krasovskii functional with multiple integral terms and employing the proposed stochastic integral inequalities and the (reciprocal) convex combination technique. The obtained stability criteria are described in terms of linear matrix inequalities, which can be easily verified by using standard software tools. Finally, three numerical examples are provided to test and verify the effectiveness and less conservativeness of the proposed stability criteria.