Cohen–Grossberg neural networks with delays provide a very powerful tool in the study of information processing, parallel computation, pattern recognition and solving of optimization problems. The robust stability behavior of such neural network models is essential in their numerous applications. Also, since the effect of various types of impulsive perturbations has been found to be remarkably important in the implementation of complex networks, the hybrid impulsive networks paradigm has gained increasing popularity during the last few decades. In this paper, an impulsive control strategy is proposed via variable impulsive perturbations for the robust stability with respect to manifolds for a class of Cohen–Grossberg neural networks with mixed delays and uncertain parameters. To this end, first new stability criteria are established for the nominal system under impulsive control. Then, the robust stability results are proposed. Finally, examples are considered to illustrate our impulsive control strategy. We generalize and extend some known robust stability results considering stability with respect to manifolds instead of isolated states stability.