Global exponential stability of delayed cellular neural networks with impulses

A class of delayed cellular neural networks with impulses (DCNN) is investigated in this paper. Sufficient conditions are obtained for the existence of unique and globally exponential stable equilibriums of the DCNNs with Lipschitzian activation functions without assuming their boundedness, monotonicity or differentiability, but subjected to impulsive state displacement at fixed instants of time. The sufficient conditions are easy to verify and when the impulsive jumps are absent, the results reduce to those of the non-impulsive systems. Our investigations are based on employing Banach's fixed point theorem, matrix and associated spectral theory. Our results generalize and significantly improve the previous known results due to this method. An example is given to show their feasibility and effectiveness.