New Criteria on Exponential Stability for Stochastic Delay Differential Systems Based on Vector Lyapunov Function
利用随机分析技术和M矩阵性质，建立了随机泛函微分系统的向量Razumikhin型指数稳定性定理，并应用于分析时滞递归神经网络在随机扰动下的鲁棒指数稳定性。
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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${M}$ </tex-math></inline-formula> -Matrix. Several novel stability criteria with vector <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$ {\mathscr {L}}$ </tex-math></inline-formula> -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.