Exponential convergence and Lagrange stability for impulsive Cohen–Grossberg neural networks with time-varying delays

• We discuss Lagrange stability for impulsive Cohen–Grossberg neural networks.
• We establish a new delay impulsive differential inequality.
• Some easily verified conditions of Lagrange exponential stability are obtained.
• Giving out the detail estimations of the exponential convergence ball.
• The results here generalize and improve the earlier publications.

In this paper, the problem on exponential convergence and Lagrange exponential stability for a class of delayed Cohen–Grossberg neural networks with impulses effects is investigated. To this end, a new delay impulsive differential inequality is established, which improves and generalizes previously known criteria. By using the new inequality and coupling with the Lyapunov method, several sufficient conditions are derived to guarantee the global exponential stability in Lagrange sense and exponential convergence of the state variables of the discussed delayed Cohen–Grossberg neural networks with impulses effects. Meanwhile, the framework of the exponential convergence ball in the state space with a pre-specified convergence rate is also given. Here, the existence and uniqueness of the equilibrium points need not to be considered. Finally, some numerical examples with simulation show the effectiveness of the obtained results.