Stability results for impulsive functional differential equations with infinite delay

For a family of differential equations with infinitive delay and impulses, we establish conditions for the existence of global solutions and for the global asymptotic and global exponential stabilities of an equilibrium point. The results are used to give stability criteria for a very broad family of impulsive neural network models with both unbounded distributed delays and bounded time-varying discrete delays. Most of the impulsive neural network models with delay recently studied are included in the general framework presented here.