Absolute exponential stability of neural networks with a general class of activation functions

Abstract

The authors investigate the absolute exponential stability (AEST) of neural networks with a general class of partially Lipschitz continuous (defined in Section II) and monotone increasing activation functions. The main obtained result is that if the interconnection matrix T of the network system satisfies that -T is an H-matrix with nonnegative diagonal elements, then the neural network system is absolutely exponentially stable (AEST); i.e., that the network system is globally exponentially stable (GES) for any activation functions in the above class, any constant input vectors and any other network parameters. The obtained AEST result extends the existing ones of absolute stability (ABST) of neural networks with special classes of activation functions in the literature.