New Criteria on Exponential Stability for Stochastic Delay Differential Systems Based on Vector Lyapunov Function

This paper established the vector Razumikhin-type theorem on exponential stability for stochastic functional differential systems by the stochastic analysis techniques and the property of ${M}$ -Matrix. Several novel stability criteria with vector $ {\mathscr {L}}$ -operator differential inequalities for stochastic delay differential systems, especially some of which includes the cross-item, were obtained by means of the vector Razumikhin theorem. By applying these new results, the robustness of global exponential stability of delay recurrent neural networks to random disturbed has been analyzed.