Stability of artificial neural networks with impulses

Sufficient conditions are obtained for the existence and asymptotic stability of a unique equilibrium of a Hoptield-type neural network with Lipschitzian activation functions without assuming their boundedness, monotonicity or differentiability and subjected to impulsive state displacements at fixed instants of time. Both the continuous-time and their corresponding discrete-time networks are considered. The sufficient conditions of the discrete-time network do not restrict the step-size appearing in the discretization process and these conditions approach as the step-size tends to zero those of the conditions of the continuous-time networks. The sufficient conditions are in terms of the parameters of the network only and are easy to verify; also when the impulsive jumps are absent the results reduce to those of the non-impulsive systems. (C) 2003 Elsevier Inc. All rights reserved.