Practical exponential stability with respect to $h-$manifolds of discontinuous delayed Cohen–Grossberg neural networks with variable impulsive perturbations

In the present work, we study discontinuous impulsive systems of the type of Cohen-Grossberg Neural Networks (CGNNs) with time-varying delays. The impulsive perturbations are realized not at fixed moments of time, and can be considered as control inputs. The hybrid concept of practical exponential stability with respect to specific manifolds defined by a function is introduced and studied analytically. The established results are applied to the case of Bidirectional Associative Memory (BAM) CGNNs. Lyapunov function method and the Razumikhin technique are the base of the proofs. A numerical example is also presented to demonstrate the applicability and effectiveness of the obtained stability conditions. The proposed results extend and complement some existing stability criteria for impulsive CGNNs with time-varying delays.