Exponential stability of impulsive cellular neural networks with time delay via Lyapunov functionals

This paper investigates the problem of exponential stability for a class of impulsive cellular neural networks with time delay. By dividing the network state variables into subgroups according to the characters of the neural networks, some sufficient conditions for exponential stability are derived by Lyapunov functionals and the method of variation of parameters. These conditions are given in terms of some blocks of the interconnection matrix, which extend and improve some of the known results in the literature. Our results show that impulses may be used to stabilize the cellular neural networks with time delay if they are not stable (or exponentially stable). On the other hand, if impulses are input disturbances, criteria on the magnitude and frequency of the impulses are also established to maintain the stability property of the original system. Our results generalize and improve some known results. Two examples with numerical simulations are given to illustrate our results.