Potential Effects of Delay on the Stability of a Class of Impulsive Neural Networks

Aiming at the interference of the delay term in continuous dynamics to the impulsive systems, we study the potential effects of time delay on the stability of a class of impulsive neural networks (INNs) in this paper. Two cases of delay are considered. For the case of small delay, a sufficient condition for the stability of delayed INNs is obtained by virtue of the average impulsive interval (AII) method. The derived results illustrate that within limits, the convergence rate of the system becomes larger with the increase of time delay. For another case, a strict comparison principle is proposed to prove that the impulsive system still maintains the original stability for any large but bounded delay under certain conditions. In particular, as an extension, the stability of delayed INNs for hybrid impulses containing both stabilizing and destabilizing impulses is also discussed. Finally, three examples are simulated to demonstrate the validity of the theoretical results.