Stability analysis of delayed Hopfield Neural Networks with impulses via inequality techniques

In this paper, the problem of stability for a class of time-delay Hopfield neural networks with impulsive perturbation is investigated. The existence of a unique equilibrium point is proved by using Arzelà–Ascoli׳s theorem and Rolle׳s theorem. Some sufficient stability criteria have proved that the uniform stability, the uniform asymptotic stability, the global asymptotic stability and the global exponential stability of the system, are derived from using the Lyapunov functional method and the linear matrix inequality approach by estimating the upper bound of the derivative of Lyapunov functional. The exponential convergence rate of the equilibrium point is also estimated. Finally, we analyze and interpret some numerical examples showing the efficiency of our theoretical results.