Mean-square exponential stability of stochastic Hopfield neural networks with time-varying discrete and distributed delays

In this Letter, the mean-square exponential stability problem for stochastic Hopfield neural networks with both discrete and distributed time-varying delays is investigated. By choosing a modified Lyapunov–Krasovskii functional, a delay-dependent criterion is established such that the stochastic neural network is mean-square exponentially stable. The derivative of discrete time-varying delay h(t)h(t) satisfies h˙(t)⩽η and the decay rate β   can be any finite positive value without any other constraints. The assumptions given in this Letter are more general than the conventional assumptions (i.e., h˙(t)⩽η<1 and β satisfies a transcendental equation or an inequality). Finally, numerical examples are provided to illustrate the effectiveness of the proposed sufficient conditions.