Exponential stability of delayed and impulsive cellular neural networks with partially Lipschitz continuous activation functions (Q448306)

Cellular neural networks (CNNs), initially introduced by Chua and Yang, have found many important applications in solving optimization problems, pattern recognition, and image processing, especially in static image treatment. Exponential stability of distributed delayed and impulsive cellular neural networks with partially Lipschitz continuous activation functions is investigated. Sufficient conditions are obtained for the uniqueness and exponential stability of the equilibrium point. Compared with some existing results, the method does not require global Lipschitz continuity, boundedness and monotonicity of activation functions, which demonstrates that the derived criteria are less restrictive than some existing ones and that they can be applied to more general situations. Moreover, it is worth mentioning that CCNs have been applied to pattern recognition where the stored patterns (equilibria) are given. Consequently, the derived results provide a new tool for this field by information of stored patterns. Finally, two examples with three cells are presented to illustrate that the theoretical results are not only generalization, but also improvement of some existing ones of cellular neural networks.